Separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivatives

Advances in Difference Equations

article

Zhong, Wenyong¹  Wang, Lanfang¹  Abdeljawad, Thabet² 

[1] College of Mathematics and Statistics, Jishou University;Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University;Department of Computer Science and Information Engineering, Asia University

关键词: Caputo–Fabrizio derivatives;    Nonlinear systems;    Stability;    Separation of solutions;    Convex Lyapunov functions;   

DOI  :  10.1186/s13662-020-02632-x

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This work mainly investigates the separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio fractional derivatives. An inequality ensuring the positivity of the fractional derivative at a given point is derived, by which the sufficient conditions for the separation of solutions are obtained. The comparison principle and the inequality for the fractional derivatives of convex functions are obtained, by which the approach of the convex Lyapunov functions is extended effectively to establish the criteria for the stability of solutions in the context of Caputo–Fabrizio fractional derivatives. Applications of the main results are illustrated by using examples.

【 授权许可】

CC BY