Efficient method for fractional Lévy-Feller advection-dispersion equation using Jacobi polynomials

2018/03/08 by N. H. Sweilam, Sweilam, N. H., Muner M. Abou Hasan +1
Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1803.03143

openalex publication_date 2018/03/08 · openalex created_date 2022/12/20 · openalex updated_date 2026/07/28

Abstract

In this paper, a novel formula expressing explicitly the fractional-order derivatives, in the sense of Riesz-Feller operator, of Jacobi polynomials is presented. Jacobi spectral collocation method together with trapezoidal rule are used to reduce the fractional Lévy-Feller advection-dispersion equation (LFADE) to a system of algebraic equations which greatly simplifies solving like this fractional differential equation. Numerical simulations with some comparisons are introduced to confirm the effectiveness and reliability of the proposed technique for the Lévy-Feller fractional partial differential equations.

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