Fractional calculus in the sky

被引：108

作者：

Baleanu, Dumitru ^{[1
,2
,3
]}

Agarwal, Ravi P. ^{[4
]}

机构：

[1] Cankaya Univ, Fac Arts & Sci, Dept Math, TR-06530 Ankara, Turkey

[2] Inst Space Sci, MG-23, R-76900 Magurele, Romania

[3] China Med Univ, Dept Med Res, China Med Univ Hosp, Taichung, Taiwan

[4] Texas A&M Univ Kingsville, Dept Math, 700 Univ Blvd,MSC 172, Kingsville, TX USA

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2021年 / 2021卷 / 01期

关键词：

Fractional calculus; Fractional differential equations; Fractional modelling; MODEL; REPRESENTATIONS;

D O I：

10.1186/s13662-021-03270-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Fractional calculus was born in 1695 on September 30 due to a very deep question raised in a letter of L'Hospital to Leibniz. The prophetical answer of Leibniz to that deep question encapsulated a huge inspiration for all generations of scientists and is continuing to stimulate the minds of contemporary researchers. During 325 years of existence, fractional calculus has kept the attention of top level mathematicians, and during the last period of time it has become a very useful tool for tackling the dynamics of complex systems from various branches of science and engineering. In this short manuscript, we briefly review the tremendous effect that the main ideas of fractional calculus had in science and engineering and briefly present just a point of view for some of the crucial problems of this interdisciplinary field.

引用

页数：9

共 50 条

[21]

Caputo M., 2015, Prog. Fract. Differ. Appl, V1, P73, DOI [DOI 10.12785/PFDA/010201, 10.12785/pfda/010201]

[22] On the notion of fractional derivative and applications to the hysteresis phenomena [J].

Caputo, Michele ;

Fabrizio, Mauro .

MECCANICA, 2017, 52 (13) :3043-3052

[23] A fractional calculus based model for the simulation of an outbreak of dengue fever [J].

Diethelm, Kai .

NONLINEAR DYNAMICS, 2013, 71 (04) :613-619

[24] Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions [J].

Fernandez, Arran ;

Baleanu, Dumitru ;

Srivastava, H. M. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2019, 67 :517-527

[25]

Hilfer R, 2000, Applications of Fractional Calculus in Physics, DOI [DOI 10.1142/3779, 10.1142/3779]

[26] Desiderata for Fractional Derivatives and Integrals [J].

Hilfer, Rudolf ;

Luchko, Yuri .

MATHEMATICS, 2019, 7 (02)

[27] STEADY-STATE HEAT CONDUCTION IN A MEDIUM WITH SPATIAL NON-SINGULAR FADING MEMORY Derivation of Caputo-Fabrizio Space-Fractional Derivative from Cattaneo Concept with Jeffrey's Kernel and Analytical Solutions [J].

Hristov, Jordan .

THERMAL SCIENCE, 2017, 21 (02) :827-839

[28]

Kilbas A. A., 2006, Theory and Applications of Fractional Differential Equations

[29]

Kiryakova V., 1994, Pitman Research Notes in Mathematics Series

[30]

Leibniz G. W., 1695, COMMUNICATION 0930, P301

← 1 2 3 4 5 →