New Recursive Approximations for Variable-Order Fractional Operators with Applications
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Date
2018
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Publisher
Vilnius Gediminas Tech Univ
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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.
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Keywords
Spectral Collocation Methods, Modified Generalized Laguerre Polynomials, Variable Order Fractional Integrals and Derivatives, Bagley-Torvik Equation
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Citation
Zaky, Mahmoud A...et al. (2018). "New Recursive Approximations for Variable-Order Fractional Operators with Applications", Mathematical Modelling and Analysis, Vol. 23, No. 2, pp. 227-239.
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Source
Mathematical Modelling and Analysis
Volume
23
Issue
2
Start Page
227
End Page
239