Well-posedness of fractional differential equations with variable-order Caputo-Fabrizio derivative. (September 2020)

• Record Type: Journal Article
• Authors: Zheng, Xiangcheng; Wang, Hong; Fu, Hongfei
• Is Part Of: Chaos, solitons and fractals. Volume 138(2020)
• Publication Date: 2020-09
• Subjects: Caputo-Fabrizio derivative -- Variable-order -- Fractional differential equations -- Well-posedness; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.109966
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Three Vo-CF-FDE models are proposed to eliminate the unreasonable restrictions. Well-posedness of the linear VO-CF-FODE model is strictly proved. Well-posedness of the VO-CF-TFRDE and nonlinear VO-CF-FODE models are proved. Abstract: We propose a nonlinear fractional ordinary differential equation (FODE) with variable-order Caputo-Fabrizio derivative, denoted by VO-CF-FODE, and prove its well-posedness. In particular, we prove that when the variable order is an integer at the initial time, the well-posedness of the proposed model does not require additional conditions imposed on the coefficient and the source term that is common in the context of constant-order CF-FODEs. The proposed methods are further extended to prove some well-posedness results of the corresponding linear partial differential equations.