NEW RECURSIVE APPROXIMATIONS FOR VARIABLE-ORDER FRACTIONAL OPERATORS WITH APPLICATIONS
2018 ◽
Vol 23
(2)
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pp. 227-239
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Keyword(s):
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.
2015 ◽
Vol 293
◽
pp. 312-338
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2018 ◽
Vol 56
◽
pp. 424-448
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2019 ◽
Vol 357
◽
pp. 103-122
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2013 ◽
Vol 31
(1)
◽
pp. 47-56
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2020 ◽
Vol 13
(2)
◽
pp. 452-478
Keyword(s):
2019 ◽
Vol 29
(2)
◽
pp. 023116
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2019 ◽
Vol 348
◽
pp. 377-395
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2007 ◽
Vol 84
(3)
◽
pp. 305-316
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