Clarify the physical process for fractional dynamical systems

doi:10.1007/s11071-020-05637-z

IR > 理学院

	Clarify the physical process for fractional dynamical systems
	Zhou, Ping 1; Ma, Jun1,2 ; Tang, Jun 3
	2020-05
发表期刊	Nonlinear Dynamics
ISSN	0924090X
卷号	100 期号:3 页码:2353-2364
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.
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
DOI	10.1007/s11071-020-05637-z
收录类别	EI ; SCIE
语种	英语
WOS研究方向	Engineering ; Mechanics
WOS类目	Engineering, Mechanical ; Mechanics
WOS记录号	WOS:000528423300002
出版者	Springer Science and Business Media B.V.
EI入藏号	20201808609948
EI主题词	Dynamical systems
EI分类号	921 Mathematics
来源库	Compendex
分类代码	921 Mathematics
引用统计	被引频次：131[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://ir.lut.edu.cn/handle/2XXMBERH/115635
专题	理学院
通讯作者	Ma, Jun
作者单位	1.Chongqing Univ Posts & Telecommun, Sch Sci, Chongqing 430065, Peoples R China; 2.Lanzhou Univ Technol, Dept Phys, Lanzhou 730050, Peoples R China; 3.China Univ Min & Technol, Sch Phys, Xuzhou 221116, Jiangsu, Peoples R China
第一作者单位	理学院
通讯作者单位	理学院
第一作者的第一单位	理学院
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.

条目包含的文件		下载所有文件
文件名称/大小	文献类型	版本类型	开放类型	使用许可
Zhou-2020-Clarify th（572KB）	期刊论文	出版稿	开放获取	CC BY-NC-SA	浏览下载