On the solvability of nonlocal fractional differential equations involving generalized Mittag-Leffler derivatives

Abstract

This paper investigates the existence, uniqueness, and stability of solutions for a controllability problem involving a class of fractional differential equations governed by the generalized Mittag-Leffler fractional derivative in the Caputo sense. The model incorporates a nonlinear source term, a fractional control operator, and a nonlocal initial condition. By employing fixed point techniques and fractional integral estimates, we establish sufficient conditions for the existence and uniqueness of solutions. Furthermore, we examine the Ulam-Hyers stability of the problem. To illustrate the theoretical findings, a concrete example is presented.