Browsing by Author "Panjaiyan Karthikeyann"

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    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.th
    The 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.
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    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.th
    In 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.
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    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.in
    The 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.
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    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.th
    Using 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.
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    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.th
    In 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.