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Legendre Wavelet and He's Homotopy Perturbation Methods for Linear Fractional Integro-Differential Equations
International Journal of Computer Applications
© 2015 by IJCA Journal
Volume 110 - Number 10
Year of Publication: 2015
|
10.5120/19354-1063 |
M H Saleh, A s Nagdy and M E M Alngar. Article: Legendre Wavelet and He's Homotopy Perturbation Methods for Linear Fractional Integro-Differential Equations. International Journal of Computer Applications 110(10):25-31, January 2015. Full text available. BibTeX
@article{key:article,
author = {M. H. Saleh and A.s. Nagdy and M. E. M. Alngar},
title = {Article: Legendre Wavelet and He's Homotopy Perturbation Methods for Linear Fractional Integro-Differential Equations},
journal = {International Journal of Computer Applications},
year = {2015},
volume = {110},
number = {10},
pages = {25-31},
month = {January},
note = {Full text available}
}
Abstract
In this paper, the Legendre wavelet method (LWM) and He's Homotopy perturbation method (HPM) are applied to approximate solution for linear fractional integro-differential equation with initial condition. A comparison between these methods takes place. Numerical examples are presented to illustrste the efficiency and accuracy of the proposed methods.
References
- Adam Loverro, Fractional calculus: History, Definitions and Application for the Engineer. (2004).
- D. Elliott, An asymptotic analysis of two algorithms for certain Hadamard finitepart integrals, IMA J. Numer. Anal. 13 (1993), 445-462.
- 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.
- H. Saeedi, F. Samimi, He's Homotopy perturbation method for nonlinear Ferdholm integro-differential equations of fractional order, Applied International Journal of Engineering Research and Applications. Vol. 2 (2012) 2248-9622.
- I. Podlubny, Fractional Differential Equations, Academic press, New York, 1999.
- J. -H. He, "Homotopy perturbation method: a new nonlinear analytical technique," Applied Mathematics and Computation, vol. 135, no. 1, pp. 73--79, 2003.
- J. -He, "Homotopy perturbation technique," Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257--262, 1999.
- J. -H. He, "Homotopy perturbation method with an auxiliary term," Abstract and Applied Analysis, vol. 2012, Article ID 857612, 7 pages, 2012.
- K. Diethelm, An algorithm for the numerical solution of differential equations of fractional order, Electronic Trans. Num. Ana. 5 (1997), 1-6.
- 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.
- 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.
- S. Yousefi and M. Razzaghi, Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations, Mathematics and computers in simulation 70 (2005), 1-8.