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31	Minisymposia Differential Equations	ABS-65
On A Perturbation Method for Weakly Nonlinear Delay Differential Equations Nikenasih Binatari, Wim van Horssen, Pieter Verstraten, Fajar Adi-Kusumo, and Lina Aryati Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia Department of Mathematics Education, Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta, Yogyakarta, Indonesia Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands Abstract This research presents a new perturbation approach to study delay differential equations (DDE) including infinitely many eigenvalues related to the linear DDE. The existing perturbation methods approximate the solution of the O(1)-DDE only with a finite number of eigenvalues, [1-7]. Eliminating many eigenvalues could also eliminate the possibility of secular terms occurring in the approximations due to internal resonances. The solution of the linear DDE at the O(1)-level is obtained by using the Laplace transform method. We also present comparisons of the results which are obtained from the proposed analytical, the existing method and a numerical method. By considering all the eigenvalues, it is shown that the proposed method gives much better approximations on a long timescale. Keywords: Delay Differential Equations, Perturbation Methods, Multiple time-scales Share Link | Plain Format | Corresponding Author (Nikenasih Binatari)

32	Minisymposia Differential Equations	ABS-67
Backpropagation neural networks for solving gas flow in porous media Adrianto, Zuher Syihab, Sutopo and Taufan Marhaendrajana Department of Petroleum Engineering, Faculty of Mining and Petroleum Technology, Bandung Institute of Technology Abstract Reservoir modeling is an essential tool in the petroleum industry to predict the dynamics of fluids in the subsurface over a period of time. Darcy^s law and the continuity equation serve as the governing equations for reservoir simulation. Discretization techniques transform the continuous partial differential equations (PDEs) into a large system of algebraic equations, and the classic iterative Newton method typically solves them. Despite its widespread use and success in many situations, the Newton method has several drawbacks or restrictions. These include the computer time required to generate and inverse the Jacobian matrix, the memory required to store it, and the challenges in achieving convergence due to the sensitivity of the initial estimate and the presence of large nonlinearities. This study presents an alternative approach to solving the system of linear equations that arises from hydrocarbon reservoir modeling. This linear solver employs feed-forward neural networks and consists of an input layer, two hidden layers, and an output layer. Later, we use this proposed solver to solve one-dimensional gas flow problems in a porous medium, and we verify its accuracy with a solution from the classic Newton method. The pressure solution generated by the neural network-based solver resembles the Newton method solution. The maximum absolute error for the homogeneous model is around 10^{-7} psi, whereas for the heterogeneous model, it is around 10^{-8} psi. The simulation results show that the learning rate parameter in networks influences convergence speed and accelerates weight updates. However, excessively high learning rates can cause weights to overshoot optimal values, causing instability and poor performance. Keywords: neural networks, linear solver, reservoir simulation Share Link | Plain Format | Corresponding Author (Adrianto Adrianto)

33	Minisymposia Differential Equations	ABS-98
COVID-19 Infectious Progression Based On Viral Load Salma Afifah , Mochamad Apri Faculty of Mathematics and Natural Science, Bandung Institute of Technology, Bandung 40132, Indonesia Abstract Coronavirus (COVID-19) is an infectious disease caused by a new variant of the virus, severe acute respiratory syndrome (SARS-CoV-20). According to research, more than 90% of infected individuals can spread the disease when the number of viruses in the host body reaches &#8805-1x10^5 RNA copies per mL [1]. Later, another study showed that the virus might spread about 5-6 days before the individual showed the first symptoms [2]. This fact suggests that someone who has been infected with the virus but is not aware of it can easily transmit the virus to others. Therefore, in this work, a mathematical model that describes the spread of COVID-19 that considers the number of viruses in the body is introduced by adjusting the SEIR model. In our model, the infectious people are divided into I_1 which represents the populations that can spread the virus before showing symptoms, and I_2 which represents the populations that are capable of spreading the virus after showing a symptom. In addition, we also consider that some of the infectious people are quarantined. The model is then analyzed to investigate the stability of the equilibrium points, the basic reproduction number (R_0), and finally numerical simulations are performed. From our result, we find that controlling the rate of transmission, and the quarantined (or isolated) proportion of infectious people who have shown symptoms, are important to suppress the spread of the disease. Keywords: COVID-19, viruses, Basic Reproduction Number, quarantine. Share Link | Plain Format | Corresponding Author (Salma Afifah)

34	Minisymposia Differential Equations	ABS-105
Numerical Solution of the (2+1) Dimensional Fractional-in-Space Nonlinear Schrodinger Equation Using the Split-Step Fourier Method with Strang Splitting Technique Nazaruddin Nazaruddin, Marwan Ramli, Muhammad Ikhwan, Said Munzir, Harish A Mardi Universitas Syiah Kuala Abstract The research is based on the growing need to develop advanced numerical methods for solving nonlinear partial differential equations, particularly those involving fractional derivatives, to understand and model complex physical phenomena and to design innovative technologies and systems. This study investigates the numerical solution of the Fractional-in-Space Nonlinear Schrodinger (FiSNLS) equation in (2 \(+\) 1) dimensions using the split-step Fourier method with the Strang splitting technique. The results show that the FiSNLS solutions are significantly influenced by the potential trap V and the parameter attenuation \( \alpha \). For \( V=0 \), there is no potential barrier that prevents the soliton from maintaining its original shape. However, for \(V\neq0\), the FiSNLS solutions still take the form of solitons. In contrast, for \( V=0.5(x^2+y^2), V=-0.5(x^2+y^2) \), and \( V=-0.5(x^2+y^2) \), the soliton dispersion is significant. By varying the value of \(\alpha\) to 2, e, and \(\pi\), it is observed that the value of \(\alpha\) significantly affects the pattern of dispersion of the FiSNLS solutions. The results of this study indicate that the FiSNLS solutions are significantly influenced by the potential trap V and the parameter attenuation \(\alpha\), and can be used to model nonlinear dynamics in various fields of science and engineering. Keywords: Attenuation- Fractional derivative- Potential trap- Split step Fourier. Share Link | Plain Format | Corresponding Author (Muhammad Ikhwan)

35	Minisymposia Differential Equations	ABS-112
Numerical Solutions of the Fisher-Kolmogorov-Petrovsky-Piskunov Equation on the Abundance of Chlorophyll-a in the Ocean Tarmizi Usman, Muhammad Ikhwan, Amelia Sari Department of Mathematics, Universitas Syiah Kuala Abstract Chlorophyll\(-\)a is a key parameter in enhancing primary productivity in the food chain generated through the photosynthesis process, which has significant implications in maintaining the balance of aquatic ecosystems. In this study, the Fisher\(-\)Kolmogorov\(-\)Petrovsky\(-\)Piskunov equation (Fisher\(-\)KPP) will be used to determine the dynamics of chlorophyll\(-\)a abundance in the Malacca Strait. The Fisher\(-\)KPP equation will be numerically solved using the finite difference method with the Crank\(-\)Nicholson scheme, yielding time series graph solutions. Time series graphs are effective visualizations for displaying periodically measured or observed data over time. This research aims to obtain numerical simulations of chlorophyll\(-\)a abundance in the Malacca Strait. Numerical simulations will vary boundary conditions represented as vectors. The simulations will be divided into two different cases, each using boundary conditions derived from the minimum and average values of chlorophyll\(-\)a data with latitude 4.065 North and 5.3125 North for boundary condition. Results from both cases show fluctuations in chlorophyll\(-\)a distribution in the Malacca Strait, following relatively similar trends to observed data patterns, with mean absolute errors (MAE) of 0.0831 and 0.5633 in each case, respectively. Based on the simulation results, it can be concluded that the Fisher\(-\)KPP equation with the Crank-Nicholson scheme effectively describes and produces data similar to observational data in this case study. Keywords: Chlorophyll a- Crank Nicholson- Malacca Strait- Fisher KPP. Share Link | Plain Format | Corresponding Author (Muhammad Ikhwan)

36	Minisymposia Dynamical Systems	ABS-10
NORMAL FORM OF PERIODIC FPU CHAIN OF FOUR PARTICLES WITH ALTERNATING MASSES S. Ardyanto (a) and J. M. Tuwankotta (a*) a) Bandung Institute of Technology Jalan Ganesha 10, Bandung 40132, Indonesia *jmtuwankotta[at]itb.ac.id Abstract In this paper we study the periodic Fermi-Pasta-Ulam (FPU) chain. It is a one dimensional chain of oscillators which endpoints are connected and has nearest neighbor interaction only. We specify our research by considering the chain with four particles and has alternating masses \(1, m, 1,m\). Moreover, we also consider a more general potential function in the Hamiltonian function of the system. The analysis is done by using the near identity transformation in phase space. The transformation is defined by using the flow of a linear Hamiltonian system, which is clearly symplectic so that the Hamiltonian structure can be preserved. The transformed Hamiltonian is then called in a so-called Birkhoff-Gustavson normal form. The structure as to the remaining terms in the normal form, depends on the choice of \(a = 1/m\). Due to the nature of the problem, there are some discrete symmetries in phase space which simplify the normal form further. Our main focus is to analyze the case when \(a = 1\) (homogeneous chain) and \(a = 3\). Depending on the value of the parameter, the system has topologically nonequivalent phase space which will be classified. The two cases which are considered express two different class of resonances. This is one of the reason why FPU chain is an interesting model to study. Keywords: FPU- Hamiltonian- Normal Form Share Link | Plain Format | Corresponding Author (Stephanus Ardyanto)

37	Minisymposia Dynamical Systems	ABS-14
THE DYNAMICS AT THE INTERSECTION BETWEEN THE CUSP AND BOGDANOV-TAKENS BIFURCATION Livia Owen, Johan Matheus Tuwankotta 1. Department of Mathematics, Parahyangan Catholic University, Bandung, Indonesia. 2. Department of Mathematics, Institut Teknologi Bandung, Indonesia. Abstract Consider a predator-prey type of system with non-monotonous response function, Holling Type IV, that models group defense mechanism response of the prey. A global analysis has been investigated by Broer. We are interested in the interaction between Cusp and Bogdanov-Takens bifurcation. At some point, this bifurcation collide and create a codimension 3 bifurcation. Keywords: Cusp bifurcation, Bogdanov-Takens bifurcation, codimension 3 bifurcation, Holling response function, Share Link | Plain Format | Corresponding Author (Livia Owen)

38	Minisymposia Dynamical Systems	ABS-18
Developing a computational model of axial oil flow from a porous rough hole Prin. Dr. Pragna A. Vadher, Dr. Gunamani B. Deheri, Dr. Sanjeev Kumar and Rakesh M. Patel A. Principal, Government Science College, Idar, Gujarat, India. B. Associate Professor (Retired), Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, India. C. Professor& Head, Department of Mathematics, DBOU, Agra University, Agra, Uttar Pradesh, India. D. Department of Mathematics, Gujarat Arts & Science College, Ahmedabad, Gujarat, India. Abstract &#61656- This study aims to present a new computational model for assessing how roughness affects axial flow emerging from a hole. &#61656- Christensen and Tonder^s stochastic averaging model has been employed to develop a mathematical calculation that captures the impact of roughness. &#61656- A closed-form solution for axial flow, including different physical parameters has been obtained. &#61656- Tabular results suggest that the effect of roughness with deformable surface is higher. &#61656- Additionally, it is observed that the eccentricity ratio plays a crucial role in improving bearing system. Keywords: Film thickness, Axial flow, Deformable roughness, Pressure distribution Share Link | Plain Format | Corresponding Author (RAKESH MANILAL PATEL)

39	Minisymposia Dynamical Systems	ABS-32
Investigation of resonance frequencies in undamped nonlinear microbeam with multi-frequency electrostatic excitations Mohammad Mahfuzh Shiddiq, Johan Matheus Tuwankotta, Eric Mathematics Department, Institut Teknologi Bandung Abstract Microelectromechanical systems (MEMS) are intensively and massively studied due to several advantages such as low cost and low energy consumption. In particular, the study of MEMS widely conducted using microbeams structures in many applications such as sensors, micro-conductors, switches and motors, etc. This study aims to investigate the microbeams vibration with simply supported boundary conditions subjected to multifrequency electrostatic excitations- taking into account mid-plane stretching forces but damping forces are omitted. This study applies perturbation method with multiple time scale to investigate resonance frequencies considering the influence of several parameters given in the model. The perturbation method does not involve truncating the constructed series solution, unlike the previous research that commonly performed truncation without justification. The excitation frequencies are explicitly determined without experimental research that costly and time-consuming. Keywords: Resonance frequencies, perturbation methods, multiple scale times. Share Link | Plain Format | Corresponding Author (Mohammad Mahfuzh Shiddiq)

40	Minisymposia Dynamical Systems	ABS-33
Dynamics of a Modified Sprott A System Muhammad Nuur Rohman, Johan Matheus Tuwankotta, Eric Harjanto Institut Teknologi Bandung Abstract We consider a modified Sprott A system, which is one of the 17 systems that exhibit chaotic behavior with no equilibrium, introduced by Jafari, Sprott, and Golpayegani (2013). For some parameter values, the modified system still preserves the original invariant sphere. We investigate the stability of the equilibria occured in the system using the stereographic map and prove that all orbits except the unstable equilibrium point converge to the stable equilibrium point. For some other parameter values, we found no invariant spheres and equilibrium points. Here the state space is foliated by tori, unlike the original one. Keywords: Sprott A system, invariant sphere, stereographic map, tori Share Link | Plain Format | Corresponding Author (Muhammad Nuur Rohman)

41	Minisymposia Dynamical Systems	ABS-41
Effect of Advection on the Modified Schnakenberg System Inas Hamidah (1*), Sutrima (2) 1) Department of Mathematics, Sebelas Maret University, Jalan Ir. Sutami No. 36A, Kentingan, Jebres, Surakarta 57126, Indonesia * inaas.hmdh29[at]student.uns.ac.id 2) Department of Mathematics, Sebelas Maret University, Jalan Ir. Sutami No. 36A, Kentingan, Jebres, Surakarta 57126, Indonesia Abstract The Schnakenberg system is a mathematical model that describes the diffusive dynamics of chemical reactions and the formation of space-time patterns. In this paper, we discuss a modified Schnakenberg system including the effects of advection, i.e. reaction diffusion-advection (RDA) system. Stability analysis shows that advection can change the equilibrium state and trigger transitions to complex spatial patterns or oscillatory states. This research uses theoretical analysis methods and literature studies to analyze the impact of diffusion-advection reactions on the modified Schnakenberg system. In this system, only one equilibrium point \(S(a+b,\frac{b+(a+b)^3}{c(a+b)^2})\) is found with the stability condition \(b-a<(1+c)(a+b)^3\). The results also show that advection in the modified Schnakenberg system affects the steady-state stability. Keywords: Schnakenberg system- Reaction Diffusion-Advection- Dynamics system Share Link | Plain Format | Corresponding Author (Inas Hamidah)

42	Minisymposia Dynamical Systems	ABS-47
Mathematical Framework of Polio Transmission Model with Vector and Incomplete Vaccination Nur Rahmi, Wahyuni Ekasasmita Institut Teknologi Bacharuddin Jusuf Habibie Abstract Polio, a debilitating disease caused by poliovirus, remains a significant public health challenge, particularly for children under five. Despite global efforts to expand immunization and surveillance systems, outbreaks continue due to gaps in vaccination coverage and the role of environmental vectors. This work creates a thorough analytical framework to investigate the dynamics of polio transmission, considering partial vaccination and virus-carrying vectors. The model assesses the stability of endemic and illness-free steady points and reveals that polio eradication is possible if the basic reproduction number remains less than one. Numerical simulations highlight the critical impact of complete vaccination and improved sanitation on reducing the basic reproduction number and controlling the spread of polio. Our findings underscore the necessity of rigorous vaccination programs and environmental hygiene to achieve long-term polio eradication. Keywords: Polio, mathematical model, stability, bifurcation, incomplete vaccination, vector Share Link | Plain Format | Corresponding Author (Nur Rahmi)

43	Minisymposia Dynamical Systems	ABS-63
Analysis of a Cells Repair Regulations Model of Nasopharyngeal Carcinoma Fajar Adi Kusumo(a*) , Ario Wiraya(b*) a) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Indonesia. b)Mathematics Education Study Program, Faculty of Teacher Training and Education, Universitas Sebelas Maret, Surakarta, Indonesia Abstract Nasopharyngeal Carcinoma (NPC) is a malignant cancer which is caused by the activation of Epstein-Barr Virus (EBV) via some external factors. It grows on nasopharyngeal epithelial cells. In the cells repair regulations, the p53 gene mutation can be used as the early indication of the NPC growth. Usually, the NPC growth is due to the DNA damage accumulation caused by the EBV infection. The base model of the cells repair regulations model to characterize the NPC growth is a 15 dimensional of first order ODE system and consists the proteins and enzymes reactions. However, there are some proteins that play important roles in the regulation of cell repair for metastatic NPC, i.e., ATM, p53, MDM2, and DSB. Therefore, we are able to construct a four-dimensional system of first-order ODE that has a 16-dimensional parameter space to study behaviours of the system and the appearance of attracting patterns of the solutions near the steady-state conditions. In this case, we use the codimension 1 and codimension 2 bifurcations analysis to study the role of several important parameters for the metastasis of NPC and study the possibilities of the system to have chaotic solutions. The appearance of a chaotic solution shows the irregularity of the system due to the changes of the initial conditions. It is important to understand the metastasis behavior NPC and to determine the treatment strategies. Keywords: Cell Repair Regulations, DNA Damage, NPC, Metastasis, Bifurcation, Torus, Homoclinic, Codimension Share Link | Plain Format | Corresponding Author (Fajar Adi Kusumo)

44	Minisymposia Dynamical Systems	ABS-64
Stability of Fluctating Baby-Skyrme Brane Emir Syahreza Fadhilla, Bobby Eka Gunara, Agus Suroso, Ardian Nata Atmaja Institut Teknologi Bandung- Pusat Riset Fisika Kuantum Badan Riset dan Inovasi Nasional Abstract This work studies the stability of fluctuating Baby-Skyrme brane as a model for early-time cosmology. The dynamical system consists of two dynamical quantities \((\phi,H)\) with two differential equations and one constraint. The solutions can be realized as a family of curves on a surface in \(\mathbb{R}^3\). We found that there exist stable solutions provided that the physical parameters \((\alpha,\sigma,k)\) satisfy certain conditions that are deduced from the linear stability conditions near the critical points. Keywords: Cosmology, Skyrme Model, Stability Share Link | Plain Format | Corresponding Author (Emir Syahreza Fadhilla)

45	Minisymposia Dynamical Systems	ABS-75
Bifurcation Analysis on Prey & Predator Model: Study on Both 2nd and 3rd Type of Holing Response Functions Gusrian Putra (a*), Dear Michiko Mutiara Noor (a), Yuslenita Muda (b), Lidya Manurung (a) a) Dept. Mathematics, Faculty of Sciences, Institut Teknologi Sumatera Jl. Terusan Ryacudu, Way Huwi, Kec. Jati Agung, Kabupaten Lampung Selatan, Lampung 35365, Indonesia *gusrian.putra[at]ma.itera.ac.id b) Dept. Mathematics, Faculty of Sciences and Technology, Universitas Islam Negeri Syarif Kasim Riau Jl. HR. Soebrantas No.Km. 15, RW.15, Simpang Baru, Kota Pekanbaru, Riau 28293 Abstract The Prey-Predator model involving Holling Type-II and Holling Type-III is investigated in detail in this paper. We begin our study by showing the positivity and boundedness of its positive solutions. The equilibria are calculated and their stability behavior are determined by means of linear stability analysis. Global stability of one of the equilibria, i.e., the interior equilibrium is investigated by means of Lyapunov function. We also provide the study of bifurcation in the model regarding the involvement of the Holling terms. Keywords: Prey-Predator mode, Holling term, Stability, Lyapunov function, bifurcation Share Link | Plain Format | Corresponding Author (Gusrian Putra)

46	Minisymposia Dynamical Systems	ABS-80
Optimization of xylitol and ethanol through the structured metabolic model of Debaryomyces hansenii Alvioni Bani(a), Kasbawati(a), Syamsuddin Toaha(a) (a) Mathematics, Hasanuddin University, Makassar, Indonesia Abstract The cellular metabolic system is an intriguing subject for research, both theoretically and experimentally, in the field of bioprocessing. The research field of understanding cellular metabolism falls within the realm of mathematics, specifically involving mathematical models. A mathematical model is utilized to address typical challenges in bioprocessing. This study investigates the intracellular metabolism of Debaryomyces hansenii, which produces xylitol and ethanol using xylose and glucose as substrates. The substrates are obtained from the pretreatment of the lignocellulosic content in oil palm empty fruit bunches. This study considers fourteen variables representing its intracellular metabolism. Further sensitivity analysis was conducted on the parameters of the system using metabolic control analysis. This involved using parameter values obtained from published research. The sensitivity analysis yielded elasticity coefficients, metabolite control coefficients on xylitol concentration, and metabolite control coefficients on ethanol concentration. The results indicated that the inlet of hemicellulose (&#945-) had the highest positive coefficient for metabolite control on xylitol concentration and ethanol concentration, and the catalysis reaction by the xylitol dehydrogenase enzyme had the highest negative coefficient for xylitol whereas the catalysis reaction by pyruvate dehydrogenase enzyme for ethanol concentration. From the numerical simulation, several regulations were applied for increasing both products i.e. xylitol and ethanol, the best ways to increase the concentrations are by increasing the inlet of hemicellulose and increasing e_5^s reaction or catalysis by xylose reductase. Keywords: Oil Palm Empty Fruit Bunches, Debaryomyces hansenii, Enzyme, Metabolic Control Analysis Share Link | Plain Format | Corresponding Author (Alvioni Bani)

47	Minisymposia Dynamical Systems	ABS-110
Optimal Control of a Mathematical Model for the Spread of Mpox Disease with Habitual Factors and Antiviral Treatment Tarmizi Usman (a), Muhammad Ikhwan (a), Putri Nabila Ikhsani (a), Said Munzir (a), Basri A Gani (b) (a) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Syiah Kuala (b) Department of Oral Biology, Faculty of Dentistry, Universitas Syiah Kuala Abstract The increase in the number of mpox infection cases in non-endemic regions in 2022 made this disease a global emergency. The United States became one of the non-endemic regions affected by mpox virus exposure. This paper aims to analyze the dynamic of mpox spread before and after control. The dynamics of mpox transmission can be represented in a mathematical model. The mathematical model consists of two populations, namely the animal population and the human population. Additionally, the model divides the human population into high risk and low risk groups, based on the level of risk for complications and mortality post-infection. The model will be controlled with habitual factors (\(u_1\)) and the administration of antivirals (\(u_2\)). Numerical simulations were conducted on three different cases to obtain optimal results. The main focus of the simulation is to observe the behavior of transmission before and after control measures are applied. The results of simulations in all cases indicate that habitual factors and antiviral treatment can minimize the spread of mpox disease. Keywords: Antiviral Control- Dynamic- Habitual Control- Mathematical Model- Mpox. Share Link | Plain Format | Corresponding Author (Muhammad Ikhwan)

48	Minisymposia Dynamical Systems	ABS-116
Analysis and Existence of Optimal Control of Diffusion Systems in Three Types of Products Alvian Alif Hidayatullah (a*), Anggi Lestari Lastiur Sitorus (a), Laylatus Syarifah (a), Subchan Subchan (a) a) Department of Mathematics, Institut Teknologi Sepuluh Nopember, Surabaya, indonesia *alvianalifhidayatullah[at]gmail.com Abstract Diffusion of innovation has an important role in the economic growth and progress of a country by spreading innovation through communication or other media in the social system. In the business environment, every company competes to present advantages and benefits in the products or services offered to achieve maximum profits. In everyday life, we often find products of the same type with different prices, quality and popularity, thus creating variations in consumer choices. Products with low prices can certainly be reached by various groups. However, products with high prices may not necessarily be accessible to various groups. It also doesn^t escape that some consumers are sometimes disappointed with a product. Therefore, in this research, a product innovation diffusion control model was constructed by providing control to each population of product users so that it does not move to a population that is disappointed with the product. There are several populations in this research, such as a population of non-users, a population of users of products with low prices, a population of users of products with high prices and a population who are disappointed with the product. This research discusses the analysis of positivity, uniqueness and the existence of optimal control in product diffusion control systems. Positivity is intended to indicate whether the model is valid, uniqueness indicates that the system has a unique solution, and the existence of optimal control aims to determine whether the product diffusion system model with control has optimal control or not. Keywords: Diffusion of innovation- Positivity- Uniqueness- Existence of optimal control Share Link | Plain Format | Corresponding Author (Alvian Alif Hidayatullah)

49	Minisymposia Dynamical Systems	ABS-129
Dynamics of the Double-Well Duffing System Wilson Gregory, Johan Matheus Tuwankotta, Eric Harjanto Department of Mathematics, Institut Teknologi Bandung Abstract We consider a Duffing system with double-well potential beam system by F. C. Moon and P. J. Holmes (1979). When there is no forcing, we study the stability of the system with and without small damping. Furthermore, the solution of the unforced system will always bounded. When the system is perturbed with a small periodic forcing, superharmonic and subharmonic cases will appear. We obtain approximations for the solution in the nonharmonic, superharmonic, and subharmonic cases which can provide the dynamics of the solution. Keywords: Duffing system, double-well potential, stability analysis, superharmonic and subharmonic responses Share Link | Plain Format | Corresponding Author (Wilson Gregory)

50	Minisymposia Fourier Analysis and Integral Operators	ABS-11
Boundedness of Szasz Operators in Half Space Wono Setya Budhi, Oki Neswan, Denny Ivanal Hakim, Ifronika Institut Teknologi Bandung Abstract Let B_n f represents the n-th Bernstein polynomial for f, for each n&#8712-N and f&#8712-C[0,1]. Then for any f&#8712-C[0,1], the sequence {B_n f} converges uniformly to f. However, for functions with continuities, the convergence may fails. A generalization of B_n, denoted by K_n, proposed by Kantorovich as an alternative. Moreover, for every f&#8712-L^p [0,1],1&#8804-p&#8804-&#8734-, {K_n f} converges to f. It is recommended to approximate integrable functions on half space [0,&#8734-) using the Szasz operator. In this paper, we show boundedness of the Szasz operators in L^p [0,&#8734-),1&#8804-p&#8804-&#8734-. Keywords: Szasz operators, Bounded operators, Share Link | Plain Format | Corresponding Author (Oki Neswan)

51	Minisymposia Fourier Analysis and Integral Operators	ABS-20
Intermediate Spaces on Weak Type Discrete Morrey Spaces Rizma Yudatama, Denny Ivanal Hakim Bandung Institute of Technology Abstract In this article we discuss inclusion between a discrete Morrey space and a weak discrete Morrey space as well as inclusion between two weak discrete Morrey spaces. By the inclusion properties of weak discrete Morrey spaces we obtain intermediate spaces for the trivial case. Using the inclusion relation of discrete Morrey spaces and weak discrete Morrey spaces, we obtain that for the nontrivial case there is no weak discrete Morrey space between Banach pairs of weak discrete Morrey spaces except for the two weak discrete Morrey spaces itself. Keywords: discrete Morrey spaces, weak discrete Morrey spaces, inclusion, intermediate spaces Share Link | Plain Format | Corresponding Author (Rizma Yudatama)

52	Minisymposia Fourier Analysis and Integral Operators	ABS-36
Rate of Convergence of the Kantorovich Operator Near \(L^1\) Abdul Karim Munir Aszari,Denny Ivanal Hakim Institut Teknologi Bandung Abstract The study of the rate of convergence of the Kantorovich operator has predominantly focused on the \(L^p\) spaces, yet the behaviour near \(L^1\) remains less understood, particularly as \(p\) approaches \(1\). To bridge this gap, we investigate the rate of convergence within the framework of the grand Lebesgue spaces \(L^{p)}[0,1]\), which encompass all \(L^p\) spaces for \(-1<p<\infty\) but remain a subset of \(L^1\). Our approach leverages the intrinsic properties of \(L^{p)}[0,1]\) to derive new results on the convergence rate of the Kantorovich operator. Specifically, we aim to demonstrate that the Kantorovich operator exhibits a significant rate of convergence within this broader context, thereby providing insights applicable to the boundary behavior as \(p\to1\). We will then apply these findings to Holder continuous functions to further understand the rate of convergence of the Kantorovich operator in these settings. This combined approach suggests that functions with derivatives in \(L^{p)}\) exhibit specific convergence rates under the Kantorovich operator. Keywords: Kantorovich operator,maximal operator,Hardy-Littlewood,Lebesgue spaces,grand Lebesgue spaces Share Link | Plain Format | Corresponding Author (Abdul Karim Munir Aszari)

53	Minisymposia Fourier Analysis and Integral Operators	ABS-37
Some Estimates for Fractional Integral Operators on Hypergroups Idha Sihwaningrum , Ari Wardayani , Mutia Nur Estri, Indra Herdiana Jenderal Soedirman University Abstract Some estimates for fractional integral operators are presented on Morrey spaces and their generalization over commutative hypergroups. Furthermore, we extend these results for the generalized fractional integral operators. Keywords: hypergroups, fractional integral operators, generalized, Morrey spaces, Share Link | Plain Format | Corresponding Author (Idha Sihwaningrum)

54	Minisymposia Fourier Analysis and Integral Operators	ABS-39
On the relation between mixed Morrey spaces and mixed Morrey double-sequence spaces Hendra Gunawan(a), Eder Kikianty(b), Denny Ivanal Hakim(a*), Ifronika(a), Rizma Yudatama(a) a)Analysis and Geometry Group, Bandung Institute of Technology. Jalan Ganesha 10, Bandung, Indonesia b)Department of Mathematics and Applied Mathematics, University of Pretoria, Private bag X20 Hatfield, 0028 Pretoria, South Africa Abstract In this article, we prove that mixed Morrey double-sequence spaces can be realized as a subspace of mixed Morrey spaces. Our proof extends a similar result for discrete Morrey spaces, obtained by Kikianty and Schwanke in 2019. As an application, we reprove several inclusion results in mixed Morrey spaces and mixed Morrey double-sequence spaces. Keywords: Mixed Morrey spaces- Mixed Morrey double sequence spaces- inclusion Share Link | Plain Format | Corresponding Author (Denny Ivanal Hakim)

55	Minisymposia Fourier Analysis and Integral Operators	ABS-53
Stein Weiss Inequality on Morrey-Adams Spaces Daniel Salim Universitas Katolik Parahyangan Abstract Stein-Weiss inequality can be considered as the boundedness of fractional integral operators on the power-weighted Lebesgue spaces. The study of Stein-Weiss inequality has developed widely for more general spaces, such as Morrey spaces and Morrey-Adams spaces. In 2024, Salim et. al. proved the Stein-Weiss inequality from local Morrey-Adams spaces into local Morrey-spaces. To continue the study, we shall consider Stein-Weiss inequality on Morrey-Adams spaces. Keywords: Stein-Weiss inequality, fractional integral operator, Morrey space, Morrey-Adams space Share Link | Plain Format | Corresponding Author (Daniel Salim)

56	Minisymposia Fourier Analysis and Integral Operators	ABS-55
Some estimates for fractional integral operators on hypergroups Idha Sihwaningrum, Ari Wardayani, Mutia Nur Estri, Indra Herdiana Jenderal Soedirman University Abstract Some estimates for fractional integral operators are presented on Morrey spaces and their generalization over commutative hypergroups. Furthermore, we extend these results for the generalized fractional integral operators. Keywords: hypergroups, fractional integral operators, generalized, Morrey spaces. Share Link | Plain Format | Corresponding Author (Mutia Nur Estri)

57	Minisymposia Fourier Analysis and Integral Operators	ABS-56
Some estimates for fractional integral operators on hypergroups Idha Sihwaningrum, Ari Wardayani, Mutia Nur Estri, Indra Herdiana Jenderal Soedirman University Abstract Some estimates for fractional integral operators are presented on Morrey spaces and their generalization over commutative hypergroups. Furthermore, we extend these results for the generalized fractional integral operators. Keywords: hypergroups, fractional integer operators, generalized, Morrey spaces, Share Link | Plain Format | Corresponding Author (Indra Herdiana)

58	Minisymposia Fourier Analysis and Integral Operators	ABS-57
Some estimates for fractional integral operators on hypergroups Idha Sihwaningrum, Ari Wardayani, Mutia Nur Estri, Indra Herdiana Jenderal Soedirman University Abstract Some estimates for fractional integral operators are presented on Morrey spaces and their generalization over commutative hypergroups. Furthermore, we extend these results for the generalized fractional integral operators. Keywords: hypergroups, fractional integral operators, generalized, Morrey spaces. Share Link | Plain Format | Corresponding Author (Ari Wardayani)

59	Minisymposia Fourier Analysis and Integral Operators	ABS-66
Embedding from Discrete Morrey Spaces to Continuous Morrey Spaces Yohanes Imanuel Runtunuwu and Hendra Gunawan Bandung Institute of Technology Abstract In this paper, we present an embedding from discrete Morrey spaces to continuous Morrey Spaces which can be seen as a refinement of the result by Yudatama (2024). We obtain the result by using a different norm on discrete Morrey spaces, which is equivalent to the existing norm. Keywords: Morrey spaces, discrete Morrey spaces, embedding Share Link | Plain Format | Corresponding Author (Yohanes Imanuel Runtunuwu)

60	Minisymposia Fourier Analysis and Integral Operators	ABS-76
Pointwise multiplier in Orlicz-Morrey spaces Ifronika, Denny Ivanal Hakim, M. Wono Setya Budhi Institut Teknologi Bandung Abstract We consider inclusion results between some Orlicz-Morrey spaces and the spaces of pointwise multiplication operators on other Orlicz-Morrey spaces. We prove that the multiplication operators are bounded from an Orlicz-Morrey spaces to another Orlicz-Morrey space under certain assumptions. We also show that a pointwise multiplier can be recognized as a member of an Orlicz-Morrey space. Our results can be seen as a generalization of those on Morrey spaces. Keywords: Morrey Spaces, Orlicz-Morrey spaces, Pointwise multiplier Share Link | Plain Format | Corresponding Author (Ifronika -)

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