Browsing by Author "Anoop Kumar"

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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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    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.in
    In 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.