Legendre wavelets approach for numerical solutions of distributed order fractional differential equations

被引：86

作者：

Yuttanan, Boonrod ^{[1
]}

Razzaghi, Mohsen ^{[2
]}

机构：

[1] Prince Songkla Univ, Fac Sci, Dept Math & Stat, Algebra & Applicat Res Unit, Hat Yai 90112, Thailand

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

来源：

APPLIED MATHEMATICAL MODELLING | 2019年 / 70卷

关键词：

Legendre wavelets; Distributed order; Fractional differential equations; Caputo derivative; OPERATIONAL MATRIX; DELAY SYSTEMS; BLOCK-PULSE; INTEGRODIFFERENTIAL EQUATIONS; HYBRID; INTEGRATION; CALCULUS; MODEL;

D O I：

10.1016/j.apm.2019.01.013

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this study, a new numerical method for the solution of the linear and nonlinear distributed fractional differential equations is introduced. The fractional derivative is described in the Caputo sense. The suggested framework is based upon Legendre wavelets approximations. For the first time, an exact formula for the Riemann-Liouville fractional integral operator for the Legendre wavelets is derived. We then use this formula and the properties of Legendre wavelets to reduce the given problem into a system of algebraic equations. Several illustrative examples are included to observe the validity, effectiveness and accuracy of the present numerical method. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：350 / 364

页数：15

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