Existence and stability results for a coupled multi-term Caputo fractional differential equations

In this article, we explore a new class of nonlocal boundary value problems defined by coupled multi-term delay Caputo fractional differential equations along with a multipoint-integral boundary problem. For analytical purposes, we reformulate the problem as a fixed-point problem to facilitate the application of fixed-point theory. The existence of solutions is demonstrated using Krasnoselskii’s fixed-point theorem, while the uniqueness of solutions is established through Banach’s fixed-point theorem. We also discuss the stability criteria, including Ulam-Hyers ( $\mathcal{UH}$ ), generalized Ulam-Hyers ( $\mathcal{GUH}$ ), Ulam-Hyers-Rassias ( $\mathcal{UHR}$ ), and generalized Ulam-Hyers-Rassias ( $\mathcal{GUHR}$ ) stability, for solutions of the equation at hand. To illustrate the theoretical results, we present an example.