Existence of Unique Stable Solutions for a system of the BVPs Involving the Caputo-Type   Modification  of Erd\'{e}lyi-Kober Fractional Derivative

Najat CHEFNAJ; Khalid Hilal; Ahmed Kajouni; Samira  ZERBIB; Asmaa  BAIHI

doi:10.5269/bspm.78453

Najat CHEFNAJ Laboratory of Applied Mathematics and Scientific Calculus Sultan Moulay Slimanne University,Beni Mellal
Khalid Hilal
Ahmed Kajouni
Samira ZERBIB
Asmaa BAIHI

Abstract

In this article, we investigate a coupled system of fractional differential equations involving the Caputo-type modification of the Erd\'{e}lyi-Kober fractional derivative. Using the Banach contraction principle, we establish the uniqueness of solutions. Furthermore, under appropriate assumptions, we apply the Leray-Schauder alternative fixed point theorem to prove the existence of at least one solution for the system. Additionally, we derive several results concerning Hyers-Ulam (H-U) stability. Finally, we provide an illustrative example to validate our findings.

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