Existence and stability results for a coupled system of Hilfer-Hadamard sequential fractional differential equations with multi-point fractional integral boundary conditions

Abstract

In this paper, we study the existence and uniqueness of solutions for a coupled system of Hilfer-Hadamard sequential fractional differential equations with multi-point Riemann-Liouville fractional integral boundary conditions via standard fixed point theorems. The existence of solutions is proved using Krasnoselskii's fixed point theorem, while the existence and uniqueness of solutions is established using the Banach fixed point theorem. We also discuss the stability of the problem in terms of Ulam-Hyers, Ulam-Hyers-Rassias, generalized Ulam-Hyers, and generalized Ulam-Hyers-Rassias stability. As an application, some examples are presented to illustrate our theoretical results.

Keywords

• fractional differential equations
• hilfer-hadamard fractional derivative
• boundary value problems
• fixed point theory
• ulam-hyers-rassias stability