Strong Ulam-Hyers Stability for a Class of Nonautonomous ψ-Caputo Fractional Differential Equations

Abstract

This article investigates the Ulam-Hyers stability of nonautonomous fractional differential equations (FDEs) with a generalized fractional derivative called the ψ-Caputo fractional derivative on the unbounded domain [a,+\∞). We introduce a special class of Ulam-Hyers stability, referred to as strong Ulam-Hyers stability for fractional dynamical systems, and establish its relationship to Lyapunov stability. It is shown that Ulam-Hyers stability is more general than Lyapunov stability. Then, we derive sufficient conditions for achieving strong Ulam-Hyers stability in both linear and nonlinear nonautonomous ψ-Caputo FDEs using the Laplace transform. Numerical example is provided to confirm the validity and applicability of the theoretical findings. Finally, by applying the main results, we establish the Ulam-Hyers stability of multi-term nonlinear ψ-Caputo FDEs. To support the obtained results, an illustrative example is presented too.