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

Abstract

Abstract 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 ( UH $\mathcal{UH}$ ), generalized Ulam-Hyers ( GUH $\mathcal{GUH}$ ), Ulam-Hyers-Rassias ( UHR $\mathcal{UHR}$ ), and generalized Ulam-Hyers-Rassias ( GUHR $\mathcal{GUHR}$ ) stability, for solutions of the equation at hand. To illustrate the theoretical results, we present an example.

Keywords

• Fixed-point
• Nonlocal integral boundary conditions
• Caputo fractional derivative
• Stability criteria