The Fixed Point Approach to the Stability of Fractional Differential Equations with Causal Operators

In this paper, the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of fractional differential equations with causal operators (FDEwCO) are investigated. The techniques rely on a fixed point theorem which is employed to study the HUR stability for FDEwCO on both bounded and unbounded time intervals as well as HU stability on bounded time interval. Finally, two typical examples are given to demonstrate the applications of theoretical results proposed.