Existence and stability results for a general class of abstract Hadamard fractional differential equations

Abstract

In this paper, we investigate a general class of abstract nonlinear fractional differential equations governed by the Hadamard fractional derivative. We establish rigorous existence and uniqueness results for mild solutions within the Banach space framework. By employing fixed-point theorems and a generalized fractional Gronwall inequality, we further demonstrate the Hadamard-type stability of the system, ensuring the continuous dependence of solutions on initial data. This abstract approach provides a unified theoretical foundation for analyzing diverse nonlinear evolution problems, substituting specific physical structures with a generalized operator-based analysis.