Some qualitative results for a new class of fractional integral equations

Abstract

n this memory, we focus on studying the issue of the existence, uniqueness and stability of solutions for a coupled systems of nonlinear integral equations under the ψ-RiemannLiouville fractional integral in some spaces endowed with vector-valued norms (generalized Banach spaces in the sense of Perov). The desired results are achieved by using a combination of fixed point theorems with vector-valued norms technique as well as convergent to zero matrices. More specifically, we essentially confirm the existence of at least one solution for the suggested problems via Schauder’s fixed-point theorem whereas the existence of a unique solution for the underlying systems is proved by Perov’s fixed-point theorem. While the concept of the matrices converging to zero is implemented to examine different types of stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, some illustrative examples are provided to demonstrate the validity of our theoretical findings.