Well-posedness of fractional differential equations with variable-order Caputo-Fabrizio derivative. (September 2020) - Zheng, Xiangcheng; Wang, Hong; Fu, Hongfei
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.