Solutions of some typical nonlinear differential equations with Caputo-Fabrizio fractional derivative

AIMS Mathematics

article

Zhoujin Cui¹ 

[1] School of Economics and Management, Jiangsu Maritime Institute;State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics

关键词: nonlinear differential equation;    Caputo-Fabrizio derivative;    nonsingular kernel;    implicit analytical solution;   

DOI  :  10.3934/math.2022779

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper, the solutions of some typical nonlinear fractional differential equations are discussed, and the implicit analytical solutions are obtained. The fractional derivative concerned here is the Caputo-Fabrizio form, which has a nonsingular kernel. The calculation results of different fractional orders are compared through images. In addition, by comparing the results obtained in this paper with those under Caputo fractional derivative, it is found that the solutions change relatively gently under Caputo-Fabrizio fractional derivative. It can be concluded that the selection of appropriate fractional derivatives and appropriate fractional order is very important in the modeling process.

【 授权许可】

CC BY