Advancing Fractional Calculus: A Fixed-Point Strategy for Nonlinear Caputo-Hadamard Equations

Abstract

This paper investigates the existence, uniqueness, and Ulam–Hyers stability of solutions for a coupled system of nonlinear Caputo–Hadamard fractional differential equations in Banach spaces. By reformulating the boundary value problem into an equivalent integral system via the Hadamard fractional integral operator, sufficient conditions for existence and uniqueness are established using Krasnoselskii’s and Banach’s fixedpoint theorems. Within the same functional framework, Ulam–Hyers stability results are derived for the proposed system. The theoretical analysis provides a consistent and unified approach for studying nonlinear coupled fractional systems with nonlocal operators, and the validity of the assumptions is illustrated through representative examples.

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