Browsing by Author "Jiraporn Reunsumrit"
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Item A comprehensive analysis of hermiteÐhadamard type inequalities via generalized preinvex functions(MDPI, 2021) Muhammad Tariq; Hijaz Ahmad; HŸseyin Budak; Soubhagya Kumar Sahoo; Thanin Sitthiwirattham; Jiraporn Reunsumrit; T. Sitthiwirattham; Department of Mathematics, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thThe principal objective of this article is to introduce the idea of a new class of n-polynomial convex functions which we call n-polynomial s-type m-preinvex function. We establish a new variant of the well-known HermiteÐHadamard inequality in the mode of the newly introduced concept. To add more insight into the newly introduced concept, we have discussed some algebraic properties and examples as well. Besides, we discuss a few new exceptional cases for the derived results, which make us realize that the results of this paper are the speculations and expansions of some recently known outcomes. The immeasurable concepts and chasmic tools of this paper may invigorate and revitalize additional research in this mesmerizing and absorbing field. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Item A new variant of Jensen inclusion and Hermite-Hadamard type inclusions for interval-valued functions(University of Nis, 2023) Thanin Sitthiwirattham; Ifra Bashir Sial; Muhammad Aamir Ali; HŸseyin Budak; Jiraporn Reunsumrit; M.A. Ali; Jiangsu Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.comIn this research, we give a new version of Jensen inclusion for interval-valued functions, which is called Jensen-Mercer inclusion. Moreover, we establish some new inclusions of the Hermite-Hadamard-Mercer type for interval-valued functions. Finally, we give some applications of newly established inequalities to make them more interesting for the readers. © 2023, University of Nis. All rights reserved.Item Analysis of Existence and Stability Results for Impulsive Fractional Integro-Differential Equations Involving the Atangana-Baleanu-Caputo Derivative under Integral Boundary Conditions(Hindawi Limited, 2022) Jiraporn Reunsumrit; Panjaiyan Karthikeyann; Sadhasivam Poornima; Kulandhaivel Karthikeyan; Thanin Sitthiwirattham; K. Karthikeyan; Department of Mathematics and Centre for Research and Development, Kpr Institute of Engineering and Technology, Coimbatore, Tamil Nadu, 641407, India; email: karthi_phd2010@yahoo.co.in; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thIn this study, we consider the existence results of solutions of impulsive Atangana-Baleanu-Caputo ABC fractional integro-differential equations with integral boundary conditions. Krasnoselskii's fixed-point theorem and the Banach contraction principle are used to prove the existence and uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end. © 2022 Jiraporn Reunsumrit et al.Item Existence Results for Impulsive Fractional Integrodifferential Equations Involving Integral Boundary Conditions(Hindawi Limited, 2022) Kulandhaivel Karthikeyan; Jiraporn Reunsumrit; Panjaiyan Karthikeyan; Sadhasivam Poornima; Dhatchinamoorthy Tamizharasan; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thThis research paper is devoted to investigating the existence results for impulsive fractional integrodifferential equations in the form of Atangana - Baleanu - Caputo (ABC) fractional derivative, by using Gronwall-Bellman inequality and Krasnoselskii's fixed point theorem to study the existence and uniqueness of the problem with integral boundary conditions. At the end, the examples are illustrated to verify results. © 2022 Kulandhaivel Karthikeyan et al.Item Existence results of fractional deltaÐnabla difference equations via mixed boundary conditions(Springer, 2020) Jiraporn Reunsumrit; 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 purpose existence results for a fractional deltaÐnabla difference equations with mixed boundary conditions by using Banach contraction principle and SchauderÕs fixed point theorem. Our problem contains a nonlinear function involving fractional delta and nabla differences. Moreover, our problem contains different orders in four fractional delta differences, four fractional nabla differences, one fractional delta sum, and one fractional nabla sum. Finally, we present some illustrative examples. © 2020, The Author(s).Item EXTENSION of HAAR WAVELET TECHNIQUES for MITTAG-LEFFLER TYPE FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS(World Scientific, 2023) Jiraporn Reunsumrit; Kamal Shah; Aziz Khan; Rohul Amin; Israr Ahmad; Thanin Sitthiwirattham; A. Khan; Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia; email: akhan@psu.edu.saFractional order integro-differential equation (FOIDE) of Fredholm type is considered in this paper. The mentioned equations have many applications in mathematical modeling of real world phenomenon like image and signal processing. Keeping the aforementioned importance, we study the considered problem from two different aspects which include the existence theory and computation of numerical approximate solution. FOIDEs have been investigated very well by using Caputo-Type derivative for the existence theory and numerical solutions. But the mentioned problems have very rarely considered under the Mittage-Leffler-Type derivative. Also, for FOIDE of Fredholm type under Mittage-Leffler-Type derivative has not yet treated by using Haar wavelet (HW) method. The aforementioned derivative is non-singular and nonlocal in nature as compared to classical Caputo derivative of fractional order. In many cases, the nonsingular nature is helpful in numerical computation. Therefore, we develop the existence theory for the considered problem by using fixed point theory. Sufficient conditions are established which demonstrate the existence and uniqueness of solution to the proposed problem. Further on utilizing HW method, a numerical scheme is developed to compute the approximate solution. Various numerical examples are given to demonstrate the applicability of our results. Also, comparison between exact and numerical solution for various fractional orders in the considered examples is given. Numerical results are displayed graphically. © 2023 The Author(s).Item HermiteÐhadamardÐmercer-type inequalities for harmonically convex mappings(MDPI, 2021) Xuexiao You; Muhammad Aamir Ali; HŸseyin Budak; Jiraporn Reunsumrit; Thanin Sitthiwirattham; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thIn this paper, we prove HermiteÐHadamardÐMercer inequalities, which is a new version of the HermiteÐHadamard inequalities for harmonically convex functions. We also prove HermiteÐ HadamardÐMercer-type inequalities for functions whose first derivatives in absolute value are harmonically convex. Finally, we discuss how special means can be used to address newly discovered inequalities. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Item Impact of bioconvection and chemical reaction on MHD nanofluid flow due to exponential stretching sheet(MDPI, 2021) Muhammad Imran Asjad; Noman Sarwar; Bagh Ali; Sajjad Hussain; Thanin Sitthiwirattham; Jiraporn Reunsumrit; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thThermal management is a crucial task in the present era of miniatures and other gadgets of compact heat density. This communication presents the momentum and thermal transportation of nanofluid flow over a sheet that stretches exponentially. The fluid moves through a porous matrix in the presence of a magnetic field that is perpendicular to the flow direction. To achieve the main objective of efficient thermal transportation with increased thermal conductivity, the possible settling of nano entities is avoided with the bioconvection of microorganisms. Furthermore, thermal radiation, heat source dissipation, and activation energy are also considered. The formulation in the form of a partial differential equation is transmuted into an ordinary differential form with the implementation of appropriate similarity variables. Numerical treatment involving RungeÐKutta along with the shooting technique method was chosen to resolve the boundary values problem. To elucidate the physical insights of the problem, computational code was run for suitable ranges of the involved parameters. The fluid temperature directly rose with the buoyancy ratio parameter, Rayleigh number, Brownian motion parameter, and thermophoresis parameter. Thus, thermal transportation enhances with the inclusion of nano entities and the bioconvection of microorganisms. The findings are useful for heat exchangers working in various technological processors. The validation of the obtained results is also assured through comparison with the existing result. The satisfactory concurrence was also observed while comparing the present symmetrical results with the existing literature. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Item New integral inequalities via generalized preinvex functions(MDPI, 2021) Muhammad Tariq; Asif Ali Shaikh; Soubhagya Kumar Sahoo; Hijaz Ahmad; Thanin Sitthiwirattham; Jiraporn Reunsumrit; T. Sitthiwirattham; Department of Mathematics, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thThe theory of convexity plays an important role in various branches of science and engineering. The objective of this paper is to introduce a new notion of preinvex functions by unifying the n-polynomial preinvex function with the s-type m-preinvex function and to present inequalities of the Hermite-Hadamard type in the setting of the generalized s-type m-preinvex function. First, we give the definition and then investigate some of its algebraic properties and examples. We also present some refinements of the Hermite-Hadamard-type inequality using HšlderÕs integral inequality, the improved power-mean integral inequality, and the Hšlder-__can integral inequality. Finally, some results for special means are deduced. The results established in this paper can be considered as the generalization of many published results of inequalities and convexity theory. © 2021 by the authors.Item On Generalization of Different Integral Inequalities for Harmonically Convex Functions(MDPI, 2022) Jiraporn Reunsumrit; Miguel J. Vivas-Cortez; Muhammad Aamir Ali; Thanin Sitthiwirattham; M.J. Vivas-Cortez; Escuela de Ciencias Matem‡ticas y F’sicas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Cat—lica del Ecuador, Quito, Av. 12 de Octubre 1076, Apartado, 17-01-2184, Ecuador; email: mjvivas@puce.edu.ecIn this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.Item On nonlinear fractional Hahn integrodifference equations via nonlocal fractional Hahn integral boundary conditions(American Institute of Mathematical Sciences, 2024) Nichaphat Patanarapeelert; Jiraporn Reunsumrit; Thanin Sitthiwirattham; 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.thAll authors Fractional Hahn differences and fractional Hahn integrals have various applications in fields where discrete fractional calculus plays a significant role, such as in discrete biological modeling and signal processing to handle systems with memory effects. In this study, the existence and uniqueness of solutions for a Riemann-Liouville fractional Hahn integrodifference equation with nonlocal fractional Hahn integral boundary conditions are investigated. To establish these results, we apply the Banach and Schauder fixed-point theorems. Furthermore, the Hyers-Ulam stability of solutions is studied. © 2024 the Author(s).Item On some new fractional ostrowski-and trapezoid-type inequalities for functions of bounded variations with two variables(MDPI, 2021) Thanin Sitthiwirattham; HŸseyin Budak; Hasan Kara; Muhammad Aamir Ali; Jiraporn Reunsumrit; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th; 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 first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid-and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for RiemannÐLiouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Item On the nonlocal fractional delta-nabla sum boundary value problem for sequential fractional delta-nabla sum-difference equations(MDPI AG, 2020) Jiraporn Reunsumrit; 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 sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder's fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example. © 2020 by the authors.Item Some Fractional Integral Inequalities Involving Mittag-Kernels(Hindawi Limited, 2022) Xiujun Zhang; Ghulam Farid; Jiraporn Reunsumrit; Ayyaz Ahmad; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thThis paper aims to present fractional versions of Minkowski-type integral inequalities via integral operators involving Mittag-Leffler functions in their kernels. Inequalities for various kinds of well-known integral operators can be deduced by selecting specific values of involved parameters. Some particular cases of main results provide connection with the inequalities which have been published in recent years. © 2022 Xiujun Zhang et al.Item Three-point fractional h-sum boundary value problems for sequential caputo fractional h-sum-difference equations(University of Nis, 2017) Jarunee Soontharanon; Jiraporn Reunsumrit; Thanin SitthiwiratthamIn this article, we study an existence and uniqueness results for a sequential nonlinear Caputo fractional h-sum-difference equation with three-point fractional h-sum boundary conditions, by using the Banach contraction principle and the Schauder�s fixed point theorem. Our problem contains different orders in three fractional difference operators and three fractional sums. Finally, we provide an example to displays the importance of these results. � 2017, University of Nis. All rights reserved.