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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

IMPACT FACTOR 2017: 1.162

CiteScore 2017: 1.41

SCImago Journal Rank (SJR) 2017: 0.382
Source Normalized Impact per Paper (SNIP) 2017: 0.636

Mathematical Citation Quotient (MCQ) 2017: 0.12

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Volume 19, Issue 7-8


Two-Dimensional Legendre Wavelets for Solving Variable-Order Fractional Nonlinear Advection-Diffusion Equation with Variable Coefficients

M. Hosseininia / M. H. Heydari / Z. Avazzadeh / F. M. Maalek Ghaini
Published Online: 2018-10-23 | DOI: https://doi.org/10.1515/ijnsns-2018-0168


This article studies a numerical scheme for solving two-dimensional variable-order time fractional nonlinear advection-diffusion equation with variable coefficients, where the variable-order fractional derivative is in the Caputo type. The main idea is expanding the solution in terms of the 2D Legendre wavelets (2D LWs) where the variable-order time fractional derivative is discretized. We describe the method using the matrix operators and then implement it for solving various types of fractional advection-diffusion equations. The experimental results show the computational efficiency of the new approach.

Keywords: variable-order fractional derivative; variable-order fractional advection-diffusion equation; variable coefficients; Legendre wavelets (LWs); finite difference scheme

MSC 2010: 34A08


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About the article

Received: 2018-06-11

Accepted: 2018-09-13

Published Online: 2018-10-23

Published in Print: 2018-12-19

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 7-8, Pages 793–802, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2018-0168.

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