Hyers-Ulam Stability and Existence of Solutions for Weighted Caputo-Fabrizio Fractional Differential Equations

Abstract In this paper, we study Hyers-Ulam stability and generalized Hyers-Ulam stability of linear equations with weighted Caputo-Fabrizio fractional derivative. We establish existence and uniqueness of solutions for nonlinear equations using Schaefer’s fixed point theorem. In addition, we present a generalized Hyers-Ulam stability result via the Gronwall inequality. Finally, two examples are given to illustrate our main results.