×

Solution of system of fractional differential equations by Adomian decomposition method. (English) Zbl 1125.26008

Summary: The aim of this paper is to apply the relatively new Adomian decomposition method to solving the system of linear fractional, in the sense of Riemann-Liouville and Caputo respectively, differential equations. The solutions are expressed in terms of Mittag-Leffler functions of matric argument. The Adomian decomposition method is straight forward, applicable for broader problems and avoids the difficulties in applying integral transforms. As the order is 1, the result here is simplified to that of first order differential equation.

MSC:

26A33 Fractional derivatives and integrals
45K05 Integro-partial differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Podlubny I. Fractional Differential Equations, San Diego: AcademicPress, 1999. · Zbl 0924.34008
[2] Miller K S, Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations, New York: Wiley, 1993. · Zbl 0789.26002
[3] Shimizu N, Zhang W. Fractional calculus approach to dynamic problems of viscoelastic materials, JSME Series C-Mechanical Systems, Machine Elements and Manufacturing, 1999, 42: 825–837.
[4] Duan J S. Time-and space-fractional partial differential equations, J Math Phys, 2005, 46: 13504–13511. · Zbl 1076.26006 · doi:10.1063/1.1819524
[5] Adomian G. Nonlinear Stochastic Operator Equations, New York: Academic Press, 1986. · Zbl 0609.60072
[6] Saha Ray S, Poddar B P, Bera R K. Analytical solution of a dynamic system containing fractional derivative of order 1/2 by Adomian decomposition method, ASME J Appl Mech, 2005, 72: 290–295. · Zbl 1111.74611 · doi:10.1115/1.1943437
[7] Saha Ray S, Bera R K. Analytical solution of the Bagley Torvik equation by Adomian decomposition method, Appl Math Comput, 2005, 168: 398–410. · Zbl 1109.65072 · doi:10.1016/j.amc.2004.09.006
[8] Saha Ray S, Bera R K. An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method, Appl Math Comput, 2005, 167: 561–571. · Zbl 1082.65562 · doi:10.1016/j.amc.2004.07.020
[9] Atanackovic T M, Stankovic B. On a system of differential equations with fractional derivatives arising in rod theory, J Phys A, 2004, 37: 1241–1250. · Zbl 1059.35011 · doi:10.1088/0305-4470/37/4/012
[10] Daftardar-Gejji V, Babakhani A. Analysis of a system of fractional differential equations, J Math Anal Appl, 2004, 293: 511–522. · Zbl 1058.34002 · doi:10.1016/j.jmaa.2004.01.013
[11] Mainardi F, Gorenflo R. On Mittag-Leffler-type functions in fractional evolution processes, J Comput Appl Math, 2000, 118: 283–299. · Zbl 0970.45005 · doi:10.1016/S0377-0427(00)00294-6
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.