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An Algorithm for the Numerical Solution of System of Fractional Differential Equations

by D.adel Sami Mohamed, Raghda Attia Mahmoud
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 65 - Number 11
Year of Publication: 2013
Authors: D.adel Sami Mohamed, Raghda Attia Mahmoud
10.5120/10970-6105

D.adel Sami Mohamed, Raghda Attia Mahmoud . An Algorithm for the Numerical Solution of System of Fractional Differential Equations. International Journal of Computer Applications. 65, 11 ( March 2013), 27-31. DOI=10.5120/10970-6105

@article{ 10.5120/10970-6105,
author = { D.adel Sami Mohamed, Raghda Attia Mahmoud },
title = { An Algorithm for the Numerical Solution of System of Fractional Differential Equations },
journal = { International Journal of Computer Applications },
issue_date = { March 2013 },
volume = { 65 },
number = { 11 },
month = { March },
year = { 2013 },
issn = { 0975-8887 },
pages = { 27-31 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume65/number11/10970-6105/ },
doi = { 10.5120/10970-6105 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:18:36.827980+05:30
%A D.adel Sami Mohamed
%A Raghda Attia Mahmoud
%T An Algorithm for the Numerical Solution of System of Fractional Differential Equations
%J International Journal of Computer Applications
%@ 0975-8887
%V 65
%N 11
%P 27-31
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we present and discuss an algorithm for the numerical solution of system of the initial value problems of the form where is the derivate of u of order , is the derivative of v of order ?in the sense of Caputo. The algorithm is based on the fractional Euler??s method which can be seen as a generalization of the classical Euler??s method.

References
  1. P. T. Torvik and R. L. Bagley, On the appearance of the fractional derivative in the behavior of real materials, J. Appl. Mech. 51 (1996), 294-298.
  2. K. B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
  3. K. S. Miller and B. Ross, 032An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, Inc. , New York, 1993.
  4. H. Beyer and S. Kemp. e, De. ntion of physically consistent damping laws with fractional derivatives, Z. Angew Math. Mech. 75 (1995), 623-635.
  5. F. Mainardi, Fractional relaxation-oscilation and fractional diffusion-wave phenomena, Chaos, Solitons & Fractals 7 (1996), 1461-1477.
  6. R. Goren. o and F. Mainardi, Fractional calculus: Integral and differential equations of fractional order. In the book Fractals and fractional calculus, (eds. : Carpinteri and Mainardi), New York, 1997.
  7. Y. Luchko and R. Gorne. o, The initial value problem for some fractional differential equations with the Caputo derivative, Fachbreich Mathematic und Informatik, Freic Universitat Berlin, (1998).
  8. I. Podlubny, Fractional differential equations, Academic Press, San Diego,CA, 1999.
  9. K. Diethelm and N. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl. 265 (2002), 229-248.
  10. F. Huang and F. Liu, The time-fractional diffusion equation and fractional advection dispersion equation, ANZIAM J. 46 (2005), 1-14.
  11. R. Goren. o, Fractional calculus: Some numerical methods. In the book Fractals and fractional calculus, (eds. : Carpinteri and Mainardi), New York, 1997.
  12. K. Diethelm, An algorithm for the numerical solution for differential equations of fractional order, Elec. Transact. Numer. Anal. 5 (1997), 1-6.
  13. A. Wazwaz, A new algorithm for calculating Adomian polynomials fo non-linear operators, Appl. Math. Comput. 111 (2000), 53-69.
  14. A. Wazwaz and S. El-Sayed, A new modi. catrion of the Adomian decomposition method for linear and nonlinear operators, Appl. Math. Comput. 122 (2001), 393-405.
  15. N. Shawagfeh, Analytical approximate solutions for nonlinear fractional differential equations, Appl. Math. Comput. 131 (2002), 517-529.
  16. S. Momani, An explicit and numerical solutions of the fractional KdV equation, Math. Comput. Simul. 70(2) (2005), 110-118.
  17. S. Momani, Non-perturbative analytical solutions of the space- and time- fractional Burgers equations, Chaos, Solitons & Fractals 28(4) (2006), 930-937.
  18. Z. Odibat and S. Momani, Approximate solutions for boundary value problems of timefractional wave equation, Appl. Math. Comput. 181(1) (2006), 767-774.
  19. Z. Odibat and S. Momani, An algorithm for the numerical solution of differential equations of fractional order, J. Appl
Index Terms

Computer Science
Information Sciences

Keywords

Generalized Taylor?s formula fractional Euler??s method fractional differential equation Caputo fractional derivative

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