Hyers-ulam stability and existence of solutions for differential equations with Caputo-Fabrizio fractional derivative

In this paper, the Hyers-Ulam stability of linear Caputo-Fabrizio fractional differential equation is established using the Laplace transform method. We also derive a generalized Hyers-Ulam stability result via the Gronwall inequality. In addition, we establish existence and uniqueness of solutions for nonlinear Caputo-Fabrizio fractional differential equations using the generalized Banach fixed point theorem and Schaefer's fixed point theorem. Finally, two examples are given to illustrate our main results.