Clarify the physical process for fractional dynamical systems

doi:10.1007/s11071-020-05637-z

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	Clarify the physical process for fractional dynamical systems
	Zhou, Ping 2; Ma, Jun 1,2; Tang, Jun 3
刊名	Nonlinear Dynamics
	2020-05-01
卷号	100 期号:3 页码:2353-2364
关键词	Algebra Calculations Differential equations Wave propagation Applied mathematics Dimensionless variables Fractional calculus Fractional differential equations Fractional dynamical systems Fractional-order systems Physical principles Physical variables
ISSN号	0924090X
DOI	10.1007/s11071-020-05637-z
英文摘要	Dynamics in fractional order systems has been discussed extensively for presenting a possible guidance in the field of applied mathematics and interdisciplinary science. Within hundreds and thousands of reviews, regular papers and drafts, many fractional differential equations are presented for enjoying mathematical proof without clarifying the scientific background and physical principles. It seems that all nonlinear problems on integer order systems even networks can be confirmed as fractional order systems. This mini-review gives an appropriate clarification on fractional dynamical systems from the physical viewpoint, thereby presenting sufficient evidences for further study on fractional calculus. We argued that non-uniform diffusion, boundary effect and elastic deformation account for the calculation and estimation with fractional order on some physical variables, which can be mapped into dimensionless variables in the dynamical systems. In addition, some similar definitions for energy, wave propagation and diffusion are suggested to find reliable confirmation in the application of fractional calculus. © 2020, Springer Nature B.V.
WOS研究方向	Engineering ; Mechanics
语种	英语
出版者	Springer Science and Business Media B.V.
WOS记录号	WOS:000528423300002
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/115635]
专题	兰州理工大学
作者单位	1.Department of Physics, Lanzhou University of Technology, Lanzhou; 730050, China; 2.School of Science, Chongqing University of Posts and Telecommunications, Chongqing; 430065, China; 3.School of Physics, China University of Mining and Technology, Xuzhou; 221116, China
推荐引用方式 GB/T 7714	Zhou, Ping,Ma, Jun,Tang, Jun. Clarify the physical process for fractional dynamical systems[J]. Nonlinear Dynamics,2020,100(3):2353-2364.
APA	Zhou, Ping,Ma, Jun,&Tang, Jun.(2020).Clarify the physical process for fractional dynamical systems.Nonlinear Dynamics,100(3),2353-2364.
MLA	Zhou, Ping,et al."Clarify the physical process for fractional dynamical systems".Nonlinear Dynamics 100.3(2020):2353-2364.