Multi-term fractional differential equations, multi-order fractional differential systems and their numerical solution

被引：15

作者：

GNS Gesellschaft für numerische Simulation mbH, Am Gauberg 2, 38114 Braunschweig, Germany ^{[1
]}

不详 ^{[2
]}

机构：

[1] GNS Gesellschaft für numerische Simulation mbH, 38114 Braunschweig

[2] Institut Computational Mathematics, Technische Universität Braunschweig, 38106 Braunschweig

来源：

J. Eur. Syst. Autom. | 2008年 / 6-8卷 / 665-676期

关键词：

Caputo derivative; Multi-order fractional differential system; Multi-term fractional differential equation; Numerical solution;

D O I：

10.3166/JESA.42.665-676

中图分类号：

学科分类号：

摘要：

Fractional differential equations containing only one fractional derivative are a well understood and frequently used tool for the mathematical description of many physical processes, but they are not always sufficient to reflect all the relevant phenomena. It is sometimes necessary to use models with more than one fractional derivative. We describe two important mathematical ways to use this concept: multi-term equations and multi-order systems. First we show the relations between these two concepts. Then we investigate their most important analytical properties, and finally we look at numerical methods for their approximate solution. © 2008 Lavoisier, Paris.

引用

页码：665 / 676

页数：11

共 15 条

[1]

Diethelm K., Predictor-corrector strategies for single-and multi-term fractional differential equations, Proceedings of the 5th Hellenic-European Conference on Computer Mathematics and its Applications, pp. 117-122, (2002)

[2]

Diethelm K., Efficient solution of multi-term fractional differential equations using P (EC) mE methods, Computing, 71, pp. 305-319, (2003)

[3]

Diethelm K., Ford N.J., Analysis of fractional differential equations, J. Math. Anal. Appl., 265, pp. 229-248, (2002)

[4]

Diethelm K., Ford N.J., Numerical solution of the Bagley-Torvik equation, BIT, 42, pp. 490-507, (2002)

[5]

Diethelm K., Ford N.J., Multi-order fractional differential equations and their numerical solution, Appl. Math. Comput., 154, pp. 621-640, (2004)

[6]

Edwards J.T., Ford N.J., Simpson A.C., The numerical solution of linear multi-term fractional differential equations: Systems of equations, J. Comput. Appl. Math., 148, pp. 401-418, (2002)

[7]

Ford N.J., Simpson A.C., The approximate solution of fractional differential equations of order greater than 1, Proceedings of the 16th IMACS World Congress on Scientific Computation, pp. 213-211, (2000)

[8]

Gorenflo R., Mainardi F., Fractional calculus: Integral and differential equations of fractional order, Fractals and Fractional Calculus in Continuum Mechanics, pp. 223-276, (1997)

[9]

Koeller R.C., Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics, Acta Mech., 58, pp. 251-264, (1986)

[10]

Linz P., Analytical and NumericalMethods for Volterra Equations, (1985)

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