On a Nonlinear Fractional Delay Differential Equation with Nonlocal Boundary Conditions

Abstract

The aim of this paper is to investigate the existence, uniqueness, and Hyers–Ulam stability of solutions to a class of nonlinear Caputo fractional delay differential equation with nonlocal boundary conditions in the space of absolutely continuous functions. Owing to the nonlinearity, the equation is not readily amenable to treatment using existing integral transform methods. Our approach employs the inverse operator technique, the multivariate Mittag-Leffler function, and several well-established fixed-point theorems. An illustrative example is provided to demonstrate the applicability of the obtained conditions. A heuristic discussion of an exact solution, together with sufficient conditions justifying the convergence of the associated formal series in the Laplace-transform domain, is also presented.