Browsing by Author "Kulandhaivel Karthikeyan"
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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 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 Analysis on Controllability Results for Impulsive Neutral Hilfer Fractional Differential Equations with Nonlocal Conditions(MDPI, 2023) Thitiporn Linitda; Kulandhaivel Karthikeyan; Palanisamy Raja Sekar; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th; K. Karthikeyan; Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, Tamil Nadu, 641407, India; email: karthikeyan.k@kpriet.ac.inIn this paper, we investigate the controllability of the system with non-local conditions. The existence of a mild solution is established. We obtain the results by using resolvent operators functions, the Hausdorff measure of non-compactness, and MonchÕs fixed point theorem. We also present an example, in order to elucidate one of the results discussed. © 2023 by the authors.Item Existence and Uniqueness of Solutions for Fractional-Differential Equation with Boundary Condition Using Nonlinear Multi-Fractional Derivatives(Hindawi Limited, 2024) Chanon Promsakon; Intesham Ansari; Mecieu Wetsah; Anoop Kumar; Kulandhaivel Karthikeyan; Thanin Sitthiwirattham; T. Sitthiwirattham; Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand; email: thanin_sit@dusit.ac.th; K. Karthikeyan; Department of Mathematics and Centre for Research and Development, Kpr Institute of Engineering and Technology, Coimbatore, Tamil Nadu, 641-407, India; email: karthi_phd2010@yahoo.co.inIn this article the existence as well as the uniqueness (EU) of the solutions for nonlinear multiorder fractional-differential equations (FDE) with local boundary conditions and fractional derivatives of different orders (Caputo and Riemann-Liouville) are covered. The existence result is derived from Krasnoselskii's fixed point theorem and its uniqueness is shown using the Banach contraction mapping principle. To illustrate the reliability of the results, two examples are given. © 2024 Chanon Promsakon 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 Solutions for Implicit Fractional Relaxation Differential Equations with Impulsive Delay Boundary Conditions(MDPI, 2022) Varaporn Wattanakejorn; Panjaiyan Karthikeyann; Sadhasivam Poornima; Kulandhaivel Karthikeyan; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th; K. Karthikeyan; Department of Mathematics, Centre for Research and Development, KPR Institute of Engineering and Technology, Coimbatore, 641407, India; email: karthi_phd2010@yahoo.co.inThe aim of this paper is to study the existence and uniqueness of solutions for nonlinear fractional relaxation impulsive implicit delay differential equations with boundary conditions. Some findings are established by applying the Banach contraction mapping principle and the Schauder fixed-point theorem. An example is provided that illustrates the theoretical results. © 2022 by the authors.Item Mild solutions for impulsive integro-differential equations involving hilfer fractional derivative with almost sectorial operators(MDPI, 2021) Kulandhaivel Karthikeyan; Panjaiyan Karthikeyan; Nichaphat Patanarapeelert; Thanin Sitthiwirattham; N. Patanarapeelert; Department of Mathematics, Faculty of Applied Science, King MongkutÕs University of Technology North Bangkok, Bangkok, 10800, Thailand; email: nichaphat.p@sci.kmutnb.ac.th; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thIn this manuscript, we establish the mild solutions for Hilfer fractional derivative integrodifferential equations involving jump conditions and almost sectorial operator. For this purpose, we identify the suitable definition of a mild solution for this evolution equations and obtain the existence results. In addition, an application is also considered. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Item On Hilfer-Type Fractional Impulsive Differential Equations(Hindawi Limited, 2022) Chanisara Metpattarahiran; Kulandhaivel Karthikeyan; Panjaiyan Karthikeyann; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thUsing the Schauder fixed point theorem, we prove the existence of impulsive fractional differential equations using Hilfer fractional derivative and nearly sectorial operators in this paper. We've gone over the two scenarios where the related semigroup is compact and noncompact for this purpose. We also go over an example to back up the main points. © 2022 Chanisara Metpattarahiran et al.Item On Implicit Atangana-Baleanu-Caputo Fractional Integro-Differential Equations with Delay and Impulses(Hindawi Limited, 2024) Panjaiyan Karthikeyann; Sadhasivam Poornima; Kulandhaivel Karthikeyan; Chanon Promsakon; Thanin Sitthiwirattham; K. Karthikeyan; Department of Mathematics, Kpr Institute of Engineering and Technology, Coimbatore, Tamil Nadu, 641407, India; email: karthi_phd2010@yahoo.co.in; T. Sitthiwirattham; Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand; email: thanin_sit@dusit.ac.thIn this paper, we study the existence and uniqueness of solutions for impulsive Atangana-Baleanu-Caputo ABC fractional integro-differential equations with boundary conditions. Schaefer's fixed point theorem and Banach contraction principle are used to prove the existence and uniqueness results. An example is presented to illustrate the results. © 2024 Panjaiyan Karthikeyann et al.