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Mathematics > Numerical Analysis

arXiv:1804.01198 (math)
[Submitted on 4 Apr 2018]

Title:New recursive approximations for variable-order fractional operators with applications

Authors:M.A. Zaky, E.H. Doha, T.M. Taha, D. Baleanu
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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.
Comments: 12 pages and 1 figure
Subjects: Numerical Analysis (math.NA)
MSC classes: 42C05, 65D99, 35R11, 65N35
Cite as: arXiv:1804.01198 [math.NA]
  (or arXiv:1804.01198v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1804.01198
Journal reference: Mathematical Modelling and Analysis 2018

Submission history

From: Mahmoud A Zaky [view email]
[v1] Wed, 4 Apr 2018 00:17:09 UTC (138 KB)
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