What is a fractional derivative?

被引：351

作者：

Ortigueira, Manuel D. ^{[1
,2
]}

Tenreiro Machado, J. A. ^{[3
]}

机构：

[1] UNL, Fac Ciencias & Tecnol, UNINOVA, P-2829516 Quinta Da Torre, Caparica, Portugal

[2] UNL, Fac Ciencias & Tecnol, DEE, P-2829516 Quinta Da Torre, Caparica, Portugal

[3] Polytech Porto, Inst Engn, Dept Elect Engn, Oporto, Portugal

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2015年 / 293卷

关键词：

Fractional derivative; Riesz potential; Fractional calculus; PROBABILITY INTERPRETATION; CALCULUS;

D O I：

10.1016/j.jcp.2014.07.019

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grunwald-Letnikov, Riemann-Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：4 / 13

页数：10

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