Well-posedness of fractional differential equations with variable-order Caputo-Fabrizio derivative

被引：21

作者：

Zheng, Xiangcheng ^{[1
]}

Wang, Hong ^{[1
]}

Fu, Hongfei ^{[2
]}

机构：

[1] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

[2] Ocean Univ China, Sch Math Sci, Qingdao 266100, Shandong, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2020年 / 138卷

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

Caputo-Fabrizio derivative; Variable-order; Fractional differential equations; Well-posedness; NUMERICAL-METHODS; VARIATIONAL-PROBLEMS; DIFFUSION-EQUATIONS;

D O I：

10.1016/j.chaos.2020.109966

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：7

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