EXISTENCE AND STABILITY RESULTS FOR COUPLED SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS INVOLVING AB-CAPUTO DERIVATIVE
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
World Scientific Publ Co Pte Ltd
Access Rights
info:eu-repo/semantics/openAccess
Abstract
In this paper, we use Krasnoselskii's fixed point theorem to find existence results for the solution of the following nonlinear fractional differential equations (FDEs) for a coupled system involving AB-Caputo fractional derivative ABC(0)D(alpha)??(l) = zeta(l,??(l),P(l)), 1 < alpha & <= 2, (SIC) AB( )C(0)D(sigma)P(l) = xi(l,??(l),P(l)), 1 < sigma <= 2,f or alll is an element of [0, 1], with boundary conditions (SIC) ??(0) = 0, lambda??'(eta) = gamma??'(1), P(0) = 0,lambda'(eta) = gamma'(1).We discuss uniqueness with the help of the Banach contraction principle. The criteria for Hyers-Ulam stability of given AB-Caputo fractional-coupled boundary value problem (BVP) is also discussed. Some examples are provided to validate our results. In Example 1, we find a unique and stable solution of AB-Caputo fractional-coupled BVP. In Example 2, the analysis of approximate and exact solutions with errors of nonlinear integral equations is elaborated with graphs.
Description
Keywords
Coupled System, AB-Caputo Fractional BVP, Existence, Uniqueness, Krasnoselskii's Fixed Point Theorem, Banach Contraction Principle, Stability
Journal or Series
Fractals-Complex Geometry Patterns and Scaling in Nature and Society
WoS Q Value
Q1
Scopus Q Value
Q1
Volume
31
Issue
2
