Hyers-Ulam stability and existence of solutions for weighted Caputo-Fabrizio fractional differential equations. (March 2020) - Wu, Xia; Chen, Fulai; Deng, Sufang
Highlights: Define Hyers-Ulam stability with weighted Caputo-Fabrizio fractional derivative. Prove Hyers-Ulam stability of linear equations using Schaefer's fixed point theorem. Establish the existence of solutions using Schaefer's fixed point theorem. Present a generalized Hyers-Ulam stability result via the Gronwall inequality. Give two examples to illustrate our main results. 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.