Hyers-Ulam stability and existence of solutions for weighted Caputo-Fabrizio fractional differential equations. (March 2020)

• Record Type: Journal Article
• Authors: Wu, Xia; Chen, Fulai; Deng, Sufang
• Is Part Of: Chaos, solitons & fractals. Volume 5(2020)
• Publication Date: 2020-03
• Subjects: Weighted Caputo-Fabrizio fractional differential equations -- Hyers-Ulam stability; 34A08 -- 34D20; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Solitons; Fractals; Chaotic behavior in systems; Periodicals; Electronic journals; 003.7
• DOI: 10.1016/j.csfx.2020.100040
• Languages: English
• ISSNs: 2590-0544

Abstract

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.