Journal of Applied Mathematics

Wavelet Collocation Method for Solving Multiorder Fractional Differential Equations

M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, and F. Mohammadi

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The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by a change of variables, the multiorder fractional differential equations (MOFDEs) with nonhomogeneous initial conditions are transformed to the MOFDEs with homogeneous initial conditions to obtain suitable numerical solution of these problems. Numerical examples are provided to demonstrate the applicability and simplicity of the numerical scheme based on the Legendre and Chebyshev wavelets.

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J. Appl. Math., Volume 2012 (2012), Article ID 542401, 19 pages.

First available in Project Euclid: 17 October 2012

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Heydari, M. H.; Hooshmandasl, M. R.; Maalek Ghaini, F. M.; Mohammadi, F. Wavelet Collocation Method for Solving Multiorder Fractional Differential Equations. J. Appl. Math. 2012 (2012), Article ID 542401, 19 pages. doi:10.1155/2012/542401.

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