Existence Results for Implicit Fractional Differential Equations with Riesz-Caputo Derivative

Abstract

This article investigates the existence and uniqueness of solutions for a class of initial value problems involving implicit fractional differential equations with the Riesz–Caputo fractional derivative. By employing fixed point theorems in conjunction with the technique of measures of noncompactness, we establish key existence and uniqueness results. Furthermore, we demonstrate that the proposed problem exhibits Ulam stability. To support and illustrate our theoretical findings, several examples are provided.