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Comparison of Adomian Decomposition and Taylor Expansion Methods for the Solutions of Fractional Integro-Differential Equations

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International Journal of Computer Applications
© 2013 by IJCA Journal
Volume 74 - Number 17
Year of Publication: 2013
Authors:
M. H. Saleh
S. M. Amer
M. A. Shalaan
10.5120/12981-0280

M H Saleh, S M Amer and M A Shalaan. Article: Comparison of Adomian Decomposition and Taylor Expansion Methods for the Solutions of Fractional Integro-Differential Equations. International Journal of Computer Applications 74(17):44-49, July 2013. Full text available. BibTeX

@article{key:article,
	author = {M. H. Saleh and S. M. Amer and M. A. Shalaan},
	title = {Article: Comparison of Adomian Decomposition and Taylor Expansion Methods for the Solutions of Fractional Integro-Differential Equations},
	journal = {International Journal of Computer Applications},
	year = {2013},
	volume = {74},
	number = {17},
	pages = {44-49},
	month = {July},
	note = {Full text available}
}

Abstract

In this paper will be compared between Adomian decomposition method (ADM) and Taylor expansion method (TEM) for solving (approximately) a class of fractional integro-differential equations. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed methods.

References

  • A. Arikoglu, I. Ozkol, Solution of fractional integro-differential equations by using fractional differential transform, Chaos, Solutions and Fractals, 40 (2009) 521-529.
  • Adam Loverro, Fractional calculus: History, Definitions and Application for the Engineer. (2004).
  • A. Wazwaz, Areliable modification of Adomian decomposition method, Applied Mathematics and Computation, 102(1) (1999) 77-86.
  • E. A. Rawashdeh, Numerical of fractional integro-differential equations by collocation method, Appl. Math. Comput. 176 (2006) 1-6.
  • E. A. Rawashdeh, Legendre Wavelet method for fractional integro-differential equations, Applied Mathematics Sciences. 5 (2011) 2467-2474.
  • F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, A carpinten and F. Mainardi (Eds), Fractals an Fractional Calulus in Continuum Mechanics, Spriger-verlag, New York, (1997) 291-348.
  • I. Podlubny, Fractional Differential Equations, Academic press, New York, 1999.
  • Jose' Paulo Carvalho dos Santos, M. Mallika Arjunan, Calaudio Cuevas, Existence results for fractional neutral integro-differential equations, Computers and Mathematics with Applications, 62 (2011) 1275-1283.
  • K. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential, Willey, New York, 1993.
  • L. Huang, X. Li, Y. Zhao, X. Duan, Approximate solution of fractional integro-differential equations by Taylor expansion method, Computers and Mathematics with Application, 62 (2011) 1127-1134.
  • M. Caputo, Linear models of dissipation whose Q is almost frequecy independent-II, Geophysical Jornal of the Royal Astronomical Society, 13 (1967) 529-539.
  • M. T. Rashed, Numerical solution of a special type of integro-differential equations, Appl. Math. Comput, 143 (2003) 73-88.
  • R. C. Mittal, R. Nigam, Solution of fractional integro-differential equations by Adomian decomposition method, Int. J. of Appl. Math. and Mech, 4 (2) (2008) 87-94.
  • S. M. Momani, local and global existence theorems integro-differential equations, Jornal of Fractional Calculus, 18 (2000) 81-86.
  • suayip Yüzbasl, Mehmer Sezer, Bayram Kemancl, Numerical solutions of integro-differential equations and application of apopulation model with an improved Legendere method, Applied Mathematics Modelling, 37 (2013) 2086-2101.
  • W. E. Olmstead, R. A. Handelsman, Diffusion in a semi-infinite region with non linear dissipation, SIAM Rev. , 18 (1976) 275-291.