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New recursive approximations for variable-order fractional operators with applications

    Mahmoud A. Zaky Affiliation
    ; Eid H. Doha Affiliation
    ; Taha M. Taha Affiliation
    ; Dumitru Baleanu Affiliation

Abstract

To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation.In this paper, we develop Laguerre spectral collocation methods for solving variable-order fractional initial value problems on the half line. Specifically, we derive three-term recurrence relations to efficiently calculate the variable-order fractional integrals and derivatives of the modified generalized Laguerre polynomials, which lead to the corresponding fractional differentiation matrices that will be used to construct the collocation methods. Comparison with other existing methods shows the superior accuracy of the proposed spectral collocation methods.

Keyword : spectral collocation methods, modified generalized Laguerre polynomials, variable order fractional integrals and derivatives, Bagley-Torvik equation

How to Cite
Zaky, M., Doha, E., Taha, T., & Baleanu, D. (2018). New recursive approximations for variable-order fractional operators with applications. Mathematical Modelling and Analysis, 23(2), 227-239. https://doi.org/10.3846/mma.2018.015
Published in Issue
Apr 18, 2018
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