Generalized fractional‐order Jacobi functions for solving a nonlinear systems of fractional partial differential equations numerically

Kamali, Farzaneh; Saeedi, Habibollah

doi:10.1002/mma.4808

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…Consequently, in the last decade, the Jacobi polynomials have been widely used to solve fractional problems. [36][37][38][39][40][41][42][43] Our method uses the Jacobi polynomials too. Thus, in this section, we briefly review the Jacobi polynomials, Jacobi quadrature rules, and a relevant theorem on the fractional derivatives of Jacobi polynomials.…”

Section: Preliminaries On Jacobi Polynomialsmentioning

confidence: 99%

A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

Almoaeet

Shamsi

Khosravian-Arab

et al. 2019

Math Methods in App Sciences

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We present the method of lines (MOL), which is based on the spectral collocation method, to solve space‐fractional advection‐diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which the SFADEs consist of both left‐ and right‐sided fractional derivatives. To do so, we begin by introducing a new set of basis functions with some interesting features. The MOL, together with the spectral collocation method based on the new basis functions, are successfully applied to the SFADEs. Finally, four numerical examples, including benchmark problems and a problem with discontinuous advection and diffusion coefficients, are provided to illustrate the efficiency and exponentially accuracy of the proposed method.

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