帮助 关于我们

返回检索结果

An Approach to Differential Geometry of Fractional Order via Modified Riemann-Liouville Derivative

查看参考文献28篇

文摘 In order to cope with some difficulties due to the fact that the derivative of a constant is not zero with the commonly accepted Riemann-Liouville definition of fractional derivative, one (Jumarie) has proposed recently an alternative referred to as (local) modified Riemann-Liouville definition, which directly, provides a Taylor's series of fractional order for non differentiable functions. We examine here in which way this calculus can be used as a framework for a differential geometry of fractional order. One will examine successively implicit function, manifold, length of curves, radius of curvature, Christoffel coefficients, velocity, acceleration. One outlines the application of this framework to Lagrange optimization in mechanics, and one concludes with some considerations on a possible fractional extension of the pseudo-geodesic of thespecial relativity and of the Lorentz transformation.
来源 Acta Mathematica Sinica. English Series ,2012,28(9):1741-1768 【核心库】
DOI 10.1007/s10114-012-0507-3
关键词 Fractional calculus ; modified Riemann-Liouville derivative ; fractional Taylor's series ; fractional manifold ; fractional geodesic ; fractional mechanics ; Lorentz transformation
地址

Department of Mathematics, University of Quebec at Montreal, Canada, Montreal, H3C 3P8

语种 英文
ISSN 1439-8516
学科 数学
文献收藏号 CSCD:4611371

参考文献 共 28 共2页

1.  Al-Akaidi M. Fractal Speech Processing,2004 CSCD被引 1 次    
2.  Almeida R. A fractional calculus of variations for multiple integrals with application to vibrating string. J. Math. Phys,2010,3:033503, 12 CSCD被引 6 次    
3.  Campos L M C. On a concept of derivative of complex order with applications to special functions. IMA J. Appl. Math,1984,33:109-133 CSCD被引 2 次    
4.  Caputo M. Linear model of dissipation whose Q is almost frequency dependent II. Geophys. J. R. Ast. Soc,1967,13:529-539 CSCD被引 62 次    
5.  Kober H. On fractional integrals and derivatives. Quart. J. Math. Oxford,1940,11:193-215 CSCD被引 2 次    
6.  Letnikov A V. Theory of differentiation of fractional order. Math. Sb,1868,3:1-7 CSCD被引 2 次    
7.  Liouville J. Sur le calcul des differentielles `a indices quelconques (in French). J. Ecole Polytechnique,1832,13:71 CSCD被引 1 次    
8.  Lv L J. The application of fractional derivatives in stochastic models driven by fractional Brownian motion. Physica A,2010,389(21):4809-4818 CSCD被引 2 次    
9.  Miller K S. An Introduction to the Fractional Calculus and Fractional Differential Equations,1933 CSCD被引 1 次    
10.  Nishimoto K. Fractional Calculus,1989 CSCD被引 2 次    
11.  Nottale L. Fractal Space Time in Microphysics,1993 CSCD被引 1 次    
12.  Oldham K B. The Fractional Calculus. Theory and Application of Differentiation and Integration to Arbitrary Order,1974 CSCD被引 1 次    
13.  Osler T J. Taylor’s series generalized for fractional derivatives and applications. SIAM J. Mathematical Analysis,1971,2(1):37-47 CSCD被引 3 次    
14.  Oustaloup A. La derivation non entiere: theorie, synthese et applications (Non-Integer Derivation: Theory, Synthesis and Applications) (in French),1995 CSCD被引 1 次    
15.  Podlubny I. Fractional Differential Equations,1999 CSCD被引 753 次    
16.  Ross B. Fractional Calculus and its Applications. Lecture Notes in Mathematics, Vol. 457,1974 CSCD被引 2 次    
17.  Samko S G. Fractional Integrals and Derivatives. Theory and Applications,1987 CSCD被引 1 次    
18.  Jumarie G. Stochastic differential equations with fractional Brownian motion input. Int. J. Syst. Sc,1993,24(6):1113-1132 CSCD被引 1 次    
19.  Jumarie G. On the representation of fractional Brownian motion as an integral with respect to (dt)~α. Applied Mathematics Letters,2005,18:739-748 CSCD被引 6 次    
20.  Jumarie G. On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion. Applied Mathematics Letters,2005,18:817-826 CSCD被引 4 次    
引证文献 2 篇

1 Abdel-Salam Emad A B Solutions to Class of Linear and Nonlinear Fractional Differential Equations Communications in Theoretical Physics,2016,65(2):127-135
CSCD被引 2 次

2 Liang Yong Shun Fractal Dimensions of Fractional Integral of Continuous Functions Acta Mathematica Sinica. English Series,2016,32(12):1494-1508
CSCD被引 2 次

显示所有2篇文献

论文科学数据集
PlumX Metrics
相关文献

 作者相关
 关键词相关
 参考文献相关

版权所有 ©2008 中国科学院文献情报中心 制作维护：中国科学院文献情报中心
地址：北京中关村北四环西路33号 邮政编码：100190 联系电话：(010)82627496 E-mail:cscd@mail.las.ac.cn 京ICP备05002861号-4 | 京公网安备11010802043238号