Browsing by Author "Saowaluck Chasreechai"
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Item A coupled system of fractional difference equations with nonlocal fractional sum boundary conditions on the discrete half-line(MDPI AG, 2019) Jarunee Soontharanon; Saowaluck Chasreechai; Thanin Sitthiwirattham; S. Chasreechai; Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand; email: saowaluck.c@sci.kmutnb.ac.thIn this article, we propose a coupled system of fractional difference equations with nonlocal fractional sum boundary conditions on the discrete half-line and study its existence result by using Schauder's fixed point theorem. An example is provided to illustrate the results. � 2019 by the authors.Item A study on the existence results of boundary value problems of fractional relaxation integro-differential equations with impulsive and delay conditions in Banach spaces(American Institute of Mathematical Sciences, 2024) Saowaluck Chasreechai; Sadhasivam Poornima; Panjaiyan Karthikeyann; Kulandhaivel Karthikeyan; Anoop Kumar; Kirti Kaushik; Thanin Sitthiwirattham; K. Karthikeyan; Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, Tamil Nadu, 641407, India; email: karthiphd2010@yahoo.co.in; T. Sitthiwirattham; Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King MongkutÕs University of Technology North Bangkok, Bangkok, 10800, Thailand; email: thanin.sit@dusit.ac.thThe aim of this paper was to provide systematic approaches to study the existence of results for the system fractional relaxation integro-differential equations. Applied problems require definitions of fractional derivatives, allowing the utilization of physically interpretable boundary conditions. Impulsive conditions serve as basic conditions to study the dynamic processes that are subject to sudden changes in their state. In the process, we converted the given fractional differential equations into an equivalent integral equation. We constructed appropriate mappings and employed the SchaeferÕs fixed-point theorem and the Banach fixed-point theorem to show the existence of a unique solution. We presented an example to show the applicability of our results. © 2024 the Author(s), licensee AIMS Press.Item Analysis of a discrete mathematical COVID-19 model(Elsevier B.V., 2021) Thanin Sitthiwirattham; Anwar Zeb; Saowaluck Chasreechai; Zohreh Eskandari; Mouhcine Tilioua; Salih Djilali; S. Djilali; Department of Mathematics, Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University, Chlef, Algeria; email: s.djilali@univ-chlef.dzTo describe the main propagation of the COVID-19 and has to find the control for the rapid spread of this viral disease in real life, in current manuscript a discrete form of the SEIR model is discussed. The main aim of this is to describe the viral disease in simplest way and the basic properties that are related with the nature of curves for susceptible and infected individuals are discussed here. The elementary numerical examples are given by using the real data of India and Algeria. © 2021 The Author(s)Item Application of asymptotic homotopy perturbation method to fractional order partial differential equation(MDPI, 2021) Haji Gul; Sajjad Ali; Kamal Shah; Shakoor Muhammad; Thanin Sitthiwirattham; Saowaluck Chasreechai; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thIn this article, we introduce a new algorithm-based scheme titled asymptotic homotopy perturbation method (AHPM) for simulation purposes of non-linear and linear differential equations of non-integer and integer orders. AHPM is extended for numerical treatment to the approximate solution of one of the important fractional-order two-dimensional Helmholtz equations and some of its cases . For probation and illustrative purposes, we have compared the AHPM solutions to the solutions from another existing method as well as the exact solutions of the considered problems. Moreover, it is observed that the symmetry or asymmetry of the solution of considered problems is invariant under the homotopy definition. Error estimates for solutions are also provided. The approximate solutions of AHPM are tabulated and plotted, which indicates that AHPM is effective and explicit. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Item Bielecki-Ulam stability of a hammerstein-type difference system(Elsevier B.V., 2025) Gul Rahmat; Sohail Ahmad; Muhammad Sarwar; Kamaleldin Abodayeh; Saowaluck Chasreechai; Thanin Sitthiwirattham; M. Sarwar; Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan; email: sarwar@uom.edu.pkIn this study, we investigate the Bielecki-Ulam (B-U) stabilities of two forms of Hammerstein-type difference systems (HT-DS). Specifically, we consider the systems: (0.1){xm+1−xm=M¯mxm+F¯(m,xm,xhm)[∑[j=0][m]G¯(m,j)H¯(j,xj,xhj)]x0=b0,and (0.2){xm+1−xm=M¯mxm+F¯(m,xm,L¯xm,J¯xm)x0=b0,by establishing conditions under which a unique solution exists. We derive sufficient conditions for the existence and uniqueness of solutions that satisfy B-U stability criteria. To demonstrate the theoretical findings, we provide an illustrative example that confirms the validity of our results. • Purpose: In this study, we examine the Bielecki-Ulam (B-U) stabilities of two forms of Hammerstein-type difference systems (HT-DS) to understand the conditions necessary for solution uniqueness and stability. • Methodology: We analyze two specific systems characterized by distinct recursive nonlinear structures and employ the Banach contraction principle under the Bielecki norm to establish stability results. The theoretical development involves verifying boundedness and Lipschitz continuity of the nonlinear terms and ensuring that the involved operators satisfy contractive conditions. • Findings: We derive sufficient conditions (outlined in Theorems 2 and 3) under which the systems possess unique solutions and are shown to be Bielecki-Ulam stable (Theorems 4 and 5). Specifically, these conditions include boundedness of system coefficients, Lipschitz continuity of nonlinear mappings, and the fulfillment of a contraction inequality using the Bielecki norm. Illustrative examples are provided to confirm the applicability of the results. © 2025 The Author(s)Item Derivation of Bounds for Majorization Differences by a Novel Method and Its Applications in Information Theory(Multidisciplinary Digital Publishing Institute (MDPI), 2023) Abdul Basir; Muhammad Adil Khan; Hidayat Ullah; Yahya Almalki; Saowaluck Chasreechai; Thanin Sitthiwirattham; M.A. Khan; Department of Mathematics, University of Peshawar, Peshawar, 25000, Pakistan; email: madilkhan@uop.edu.pk; T. Sitthiwirattham; Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King MongkutÕs University of Technology North Bangkok, Bangkok, 10800, Thailand; email: thanin_sit@dusit.ac.thIn the recent era of research developments, mathematical inequalities and their applications perform a very consequential role in different aspects, and they provide an engaging area for research activities. In this paper, we propose a new approach for the improvement of the classical majorization inequality and its weighted versions in a discrete sense. The proposed improvements give several estimates for the majorization differences. Some earlier improvements of the Jensen and Slater inequalities are deduced as direct consequences of the obtained results. We also discuss the conditions under which the main results give better estimates for the majorization differences. Applications of the acquired results are also presented in information theory. © 2023 by the authors.Item Existence and multiplicity of positive solutions to a system of fractional difference equations with parameters(Springer, 2020) Pimchana Siricharuanun; Saowaluck Chasreechai; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thWe consider a fractional difference-sum boundary problem for a system of fractional difference equations with parameters. Using the Banach fixed point theorem, we prove the existence and uniqueness of solutions. We also prove the existence of at least one and two solutions by using the KrasnoselskiiÕs fixed point theorem for a cone map. Finally, we give some examples to illustrate our results. © 2020, The Author(s).Item Existence and stability analysis for fractional impulsive caputo difference-sum equations with periodic boundary condition(MDPI AG, 2020) Rujira Ouncharoen; Saowaluck Chasreechai; Thanin Sitthiwirattham; S. Chasreechai; Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand; email: saowaluck.c@sci.kmutnb.ac.thIn this paper, by using the Banach contraction principle and the Schauder's fixed point theorem, we investigate existence results for a fractional impulsive sum-difference equations with periodic boundary conditions. Moreover, we also establish different kinds of Ulam stability for this problem. An example is also constructed to demonstrate the importance of these results. © 2020 by the authors.Item Existence of positive solution to a coupled system of singular fractional difference equations via fractional sum boundary value conditions(Springer International Publishing, 2019) Chanon Promsakon; Saowaluck Chasreechai; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, Thailand; email: thanin_sit@dusit.ac.thIn this article, we study a coupled system of singular fractional difference equations with fractional sum boundary conditions. A sufficient condition of the existence of positive solutions is established by employing the upper and lower solutions of the system and using Schauder�s fixed point theorem. Finally, we provide an example to illustrate our results. � 2019, The Author(s).Item Existence Results of Initial Value Problems for Hybrid Fractional Sum-Difference Equations(Hindawi Limited, 2018) Saowaluck Chasreechai; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, Thailand; email: thanin_sit@dusit.ac.thWe consider a hybrid fractional sum-difference initial value problem and a hybrid fractional sequential sum-difference initial value problem. The existence results of these two problems are proved by using the hybrid fixed point theorem for three operators in a Banach algebra and the generalized Krasnoselskii's fixed point theorem, respectively. � 2018 Saowaluck Chasreechai and Thanin Sitthiwirattham.Item Existence, uniqueness and controllability results of nonlinear neutral implicit ABC fractional integro-differential equations with delay and impulses(American Institute of Mathematical Sciences, 2025) Sivaranjani Ramasamy; Thangavelu Senthilprabu; Kulandhaivel Karthikeyan; Palanisamy Geetha; Saowaluck Chasreechai; Thanin Sitthiwirattham; S. Ramasamy; Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, Tamilnadu, 641 407, India; email: sivaranjanirphd@gmail.com; S. Chasreechai; Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand; email: saowaluck.c@sci.kmutnb.ac.thIn this article, the necessary and sufficient conditions for the existence and uniqueness of the mild solutions for nonlinear neutral implicit integro-differential equations of non-integer order 0 < α < 1 in the sense of ABC derivative with impulses, delay, and integro initial conditions were established. The existence results were derived using the semi-group theory, measures of non-compactness, and the fixed-point theory in the sense of Arzelà–Ascoli theorem and Schauder’s fixed-point theorem. We analyzed the controllability results of the proposed problem by incorporating the ideas of semi-group theory and fixed-point techniques. The Banach contraction principle was used to derive the uniqueness and controllability of the proposed problem. We provide an example to support the theoretical results. © 2025 the Author(s), licensee AIMS Press.Item Montgomery identity and Ostrowski-type inequalities via quantum calculus(De Gruyter Open Ltd, 2021) Thanin Sitthiwirattham; Muhammad Aamir Ali; Huseyin Budak; Mujahid Abbas; Saowaluck Chasreechai; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.comIn this paper, we prove a quantum version of Montgomery identity and prove some new Ostrowski-type inequalities for convex functions in the setting of quantum calculus. Moreover, we discuss several special cases of newly established inequalities and obtain different new and existing inequalities in the field of integral inequalities. © 2021 Thanin Sitthiwirattham et al., published by De Gruyter.Item On a coupled system of fractional sum-difference equations with p-Laplacian operator(Springer, 2020) Pimchana Siricharuanun; Saowaluck Chasreechai; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thIn this paper, we propose a nonlocal fractional sum-difference boundary value problem for a coupled system of fractional sum-difference equations with p-Laplacian operator. The problem contains both RiemannÐLiouville and Caputo fractional difference with five fractional differences and four fractional sums. The existence and uniqueness result of the problem is studied by using the Banach fixed point theorem. © 2020, The Author(s).Item On New Estimates of q-HermiteÐHadamard Inequalities with Applications in Quantum Calculus(MDPI, 2023) Saowaluck Chasreechai; Muhammad Aamir Ali; Muhammad Amir Ashraf; Thanin Sitthiwirattham; Sina Etemad; Manuel De la Sen; Shahram Rezapour; S. Etemad; Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, 3751-71379, Iran; email: sina.etemad@azaruniv.ac.ir; S. Rezapour; Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, 3751-71379, Iran; email: sh.rezapour@azaruniv.ac.ir; M.D.L. Sen; Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country (UPV/EHU), Leioa, Bizkaia, 48940, Spain; email: manuel.delasen@ehu.eusIn this paper, we first establish two quantum integral (q-integral) identities with the help of derivatives and integrals of the quantum types. Then, we prove some new q-midpoint and q-trapezoidal estimates for the newly established q-Hermite-Hadamard inequality (involving left and right integrals proved by Bermudo et al.) under q-differentiable convex functions. Finally, we provide some examples to illustrate the validity of newly obtained quantum inequalities. © 2023 by the authors.Item On nonlinear fractional difference equation with delay and impulses(MDPI AG, 2020) Rujira Ouncharoen; Saowaluck Chasreechai; Thanin Sitthiwirattham; S. Chasreechai; Department of Mathematics, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand; email: saowaluck.c@sci.kmutnb.ac.th; T. Sitthiwirattham; Mathematics Department, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thIn this paper, we establish the existence results for a nonlinear fractional difference equation with delay and impulses. The Banach and Schauder's fixed point theorems are employed as tools to study the existence of its solutions. We obtain the theorems showing the conditions for existence results. Finally, we provide an example to show the applicability of our results. © 2020 by the authors.Item On nonlocal boundary value problems for hybrid fractional sum-difference equations involving different orders(Mathematical Research Press, 2018) Saowaluck Chasreechai; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Tchology, Suan Dusit University, Bangkok, Thailand; email: thanin_sit@dusit.ac.thIn this article, we study existence results for Riemann-Liouville fractional sum-difference equations with a nonlocal fractional difference and fractional sum boundary value conditions based on the Sadovskii�s fixed point theorem. The investigated equations contain different orders of fractional differences and fractional sums. Finally, we present some examples to show the importance of these results. � 2018 Journal of Nonlinear Functional Analysis.Item On nonlocal Neumann boundary value problem for a second-order forward (_, _) -difference equation(Springer International Publishing, 2018) Thitiporn Linitda; Saowaluck Chasreechai; S. Chasreechai; Department of Mathematics, Faculty of Applied Science, King Mongkut�s University of Technology North Bangkok, Bangkok, Thailand; email: saowaluck.c@sci.kmutnb.ac.thIn this paper, we present some properties of the forward (_, _) -difference operators, and the existence results of two nonlocal boundary value problems for second-order forward (_, _) -difference equations. The existence and uniqueness results are proved by using the Banach fixed point theorem, and the existence of at least one positive solution is established by using the Krasnoselskii� fixed point theorem. � 2018, The Author(s).Item On positive solution to multi-point fractional h-sum eigenvalue problems for caputo fractional h-difference equations(University of Nis, 2018) Saowaluck Chasreechai; Jarunee Soontharanon; Thanin SitthiwiratthamIn this article, we study the existence of at least one positive solution to a multi-point fractional h-sum eigenvalue problem for Caputo fractional h-difference equation, by using the Guo-Krasnoselskii�s fixed point theorem. Moreover, we present some examples to display the importance of these results. � 2018, University of Nis. All rights reserved.Item On separate fractional sum-difference equations with n-point fractional sum-difference boundary conditions via arbitrary different fractional orders(MDPI AG, 2019) Saowaluck Chasreechai; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10700, Thailand; email: thanin_sit@dusit.ac.thIn this article, we study the existence and uniqueness results for a separate nonlinear Caputo fractional sum-difference equation with fractional difference boundary conditions by using the Banach contraction principle and the Schauder's fixed point theorem. Our problem contains two nonlinear functions involving fractional difference and fractional sum. Moreover, our problem contains different orders in n + 1 fractional differences and m + 1 fractional sums. Finally, we present an illustrative example. � 2019 by the authors.Item On some SimpsonÕs and NewtonÕs type of inequalities in multiplicative calculus with applications(American Institute of Mathematical Sciences, 2023) Saowaluck Chasreechai; Muhammad Aamir Ali; Surapol Naowarat; Thanin Sitthiwirattham; Kamsing Nonlaopon; K. Nonlaopon; Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand; email: nkamsi@kku.ac.thIn this paper, we establish an integral equality involving a multiplicative differentiable function for the multiplicative integral. Then, we use the newly established equality to prove some new SimpsonÕs and NewtonÕs inequalities for multiplicative differentiable functions. Finally, we give some mathematical examples to show the validation of newly established inequalities. © 2023 the Author(s), licensee AIMS Press.