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

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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 multiterm nonlinear ψ-Caputo FDEs. To support the obtained results, an illustrative example is presented too.