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

2025

Fixed Point Theory and Algorithms for Sciences and Engineering, Vol 2025, Iss 1, Pp 1-33 (2025)

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.

article

English

SpringerOpen, 2025.

Fixed-point, Nonlocal integral boundary conditions, Caputo fractional derivative, Stability criteria, Applied mathematics. Quantitative methods, T57-57.97, Analysis, QA299.6-433