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Wavelet Collocation Method for Solving Multiorder Fractional Differential Equations

Author

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  • M. H. Heydari
  • M. R. Hooshmandasl
  • F. M. Maalek Ghaini
  • F. Mohammadi

Abstract

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.

Suggested Citation

  • M. H. Heydari & M. R. Hooshmandasl & F. M. Maalek Ghaini & F. Mohammadi, 2012. "Wavelet Collocation Method for Solving Multiorder Fractional Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-19, February.
    • Handle: RePEc:hin:jnljam:542401
    DOI: 10.1155/2012/542401
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    Cited by:

    1. Heydari, Mohammad Hossein & Avazzadeh, Zakieh & Haromi, Malih Farzi, 2019. "A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 215-228.
    2. Waseem, Waseem & Sulaiman, M. & Aljohani, Abdulah Jeza, 2020. "Investigation of fractional models of damping material by a neuroevolutionary approach," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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