A Spectral Numerical Method for Solving Distributed-Order Fractional Initial Value Problems
2018 ◽
Vol 13
(10)
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Keyword(s):
In this paper, we construct and analyze a Legendre spectral-collocation method for the numerical solution of distributed-order fractional initial value problems. We first introduce three-term recurrence relations for the fractional integrals of the Legendre polynomial. We then use the properties of the Caputo fractional derivative to reduce the problem into a distributed-order fractional integral equation. We apply the Legendre–Gauss quadrature formula to compute the distributed-order fractional integral and construct the collocation scheme. The convergence of the proposed method is discussed. Numerical results are provided to give insights into the convergence behavior of our method.
2015 ◽
Vol 95
(9)
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pp. 1989-2003
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Keyword(s):
2012 ◽
Vol 15
(3)
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