Algorithms for the fractional calculus: A selection of numerical methods

被引：487
作者：
Diethelm, K
Ford, NJ
Freed, AD
Luchko, Y
机构：
[1] NASA, John H Glenn Res Ctr Lewis Field, Polymers Branch, Div Mat, Cleveland, OH 44135 USA
[2] Tech Univ Braunschweig, Inst Angew Math, D-38106 Braunschweig, Germany
[3] Chester Coll Higher Educ, Dept Math, Chester CH1 4BJ, Cheshire, England
[4] Cleveland Clin Fdn, Dept Biomed Engn, Lerner Res Inst, Cleveland, OH 44195 USA
[5] European Univ Frankfurt, Dept Business Informat, D-15207 Frankfurt, Germany
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2005年 / 194卷 / 6-8期
关键词：
Riemann-Liouville integrals; Caputo derivatives; Caputo differential equations; Mittag-Leffler function;
D O I：
10.1016/j.cma.2004.06.006
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
Many recently developed models in areas like viscoelasticity. electrochemistry. diffusion processes. etc are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way. Published by Elsevier B.V.
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页码：743 / 773
页数：31
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