A numerical method based on fractional-order generalized Taylor wavelets for solving distributed-order fractional partial differential equations

被引：39

作者：

Yuttanan, Boonrod ^{[1
]}

Razzaghi, Mohsen ^{[2
]}

Vo, Thieu N. ^{[3
]}

机构：

[1] Prince Songkla Univ, Fac Sci, Div Computat Sci, Algebra & Applicat Res Unit, Hat Yai 90110, Thailand

[2] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

[3] Ton Duc Thang Univ, Fac Math & Stat, Fract Calculus Optimizat & Algebra Res Grp, Ho Chi Minh City, Vietnam

来源：

APPLIED NUMERICAL MATHEMATICS | 2021年 / 160卷

关键词：

Numerical method; Taylor wavelet; Numerical solution; Fractional partial differential equation; Distributed-order differential equation; OPERATIONAL MATRIX; DIFFUSION EQUATION; PETROV-GALERKIN; CALCULUS; MODEL; APPROXIMATION; INTEGRATION;

D O I：

10.1016/j.apnum.2020.10.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a numerical method for solving distributed-order fractional partial differential equations (FPDEs). For this method, we first introduce fractional-order generalized Taylor wavelets (FOGTW). An estimation for the error of the approximation is also studied. In addition, by using the regularized beta function we give a formula for determining the Riemann-Liouville fractional integral operator for the FOGTW. Combining this formula with the Gauss-Legendre quadrature, we obtain a numerical method for solving distributed-order FPDEs. Several illustrative examples are given to show the applicability and the accuracy of the proposed method. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：349 / 367

页数：19

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