Qualitative analysis of a coupled system with nonlinear mixed fractional integro-differential equation involving Caputo fractional derivative

Volume 38, Issue 1, pp 56--79 https://dx.doi.org/10.22436/jmcs.038.01.05

Publication Date: November 21, 2024 Submission Date: September 05, 2024 Revision Date: September 22, 2024 Accteptance Date: September 29, 2024

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Authors

M. Asif - Department of Mathematics, University of Peshawar, 25000, Pakistan. A. Zada - Department of Mathematics, University of Peshawar, 25000, Pakistan. A. Avram - Department of Computing, Mathematics and Engineering, , Alba Iulia, 510 0 09, Romania.

Abstract

This paper introduces a novel model involving an integro-differential equation of fractional order characterized by multiple nonlinear terms with Caputo fractional derivatives. We derive conditions ensuring the existence, uniqueness, and stability of the mild solution. Furthermore, we explore a coupled system that includes the proposed equations and extend our analysis to an equation featuring three nonlinearities. The study utilizes Banach's, Krasnoselskii's, and Schaefer's fixed point theorems. Additionally, we investigate various forms of Hyers-Ulam stability for the equation and the coupled system. To demonstrate the practical implications of our findings, illustrative examples are provided.

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Keywords

• Caputo derivative
• Riemann-Liouville fractional integral
• existence
• fixed point
• Ulam stability

MSC

•  26A33
•  34A08
•  34B27
•  39B82

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