Journal
CHINESE JOURNAL OF PHYSICS
Volume 68, Issue -, Pages 533-541Publisher
ELSEVIER
DOI: 10.1016/j.cjph.2020.10.011
Keywords
Fractional derivative operator; Sigmoid function; Nonlinear phenomena
Categories
Funding
- Future Scientists Program of China University of Mining and Technology [2020WLKXJ037]
- Postgraduate Research & Practice Innovation Program of Jiangsu Province [No.KYCX20_1976]
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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.
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