New fractional derivative with sigmoid function as the kernel and its models

被引：24
|
作者：
Liu, Jian-Gen [1 ,2 ]
Yang, Xiao-Jun [1 ,2 ,3 ]
Feng, Yi-Ying [2 ,3 ]
Cui, Ping [2 ,4 ]
机构：
[1] China Univ Min & Technol, Sch Math, Xuzhou 221116, Jiangsu, Peoples R China
[2] China Univ Min & Technol, State Key Lab Geomech & Deep Underground Engn, Xuzhou 221116, Jiangsu, Peoples R China
[3] China Univ Min & Technol, Sch Mech & Civil Engn, Xuzhou 221116, Jiangsu, Peoples R China
[4] Qujing Normal Univ, Sch Math & Stat, Qujing 655000, Yunnan, Peoples R China
来源：
CHINESE JOURNAL OF PHYSICS | 2020年 / 68卷
关键词：
Fractional derivative operator; Sigmoid function; Nonlinear phenomena; EQUATION;
D O I：
10.1016/j.cjph.2020.10.011
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Based on the idea of the fractional derivative with respect to another function, a new fractional derivative operator with sigmoid function as the kernel in this article, is proposed for the first time. Then, we make use of this new fractional operator to model various nonlinear phenomena from different fields of applications in science, such as the population growth, the shallow water wave phenomena and reaction-diffusion processes, and so on. As a result, we hope that the new fractional operator can be used to discover more evolutionary mechanisms of these phenomena.
引用
收藏
页码：533 / 541
页数：9
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