An Application of the Gegenbauer Wavelet Method for the Numerical Solution of the Fractional Bagley-Torvik Equation

被引：72
作者：
Srivastava, H. M. [1 ,2 ]
Shah, F. A. [3 ]
Abass, R. [3 ]
机构：
[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan
[3] Univ Kashmir, Dept Math, South Campus, Anantnag 192101, Jammu & Kashmir, India
来源：
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS | 2019年 / 26卷 / 01期
关键词：
OPERATIONAL MATRIX; ORDER INTEGRATION;
D O I：
10.1134/S1061920819010096
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, a potentially useful new method based on the Gegenbauer wavelet expansion, together with operational matrices of fractional integral and block-pulse functions, is proposed in order to solve the Bagley-Torvik equation. The Gegenbauer wavelets are generated here by dilation and translation of the classical orthogonal Gegenbauer polynomials. The properties of the Gegenbauer wavelets and the Gegenbauer polynomials are first presented. These functions and their associated properties are then employed to derive the Gegenbauer wavelet operational matrices of fractional integrals. The operational matrices of fractional integrals are utilized to reduce the problem to a set of algebraic equations with unknown coefficients. Illustrative examples are provided to demonstrate the validity and applicability of the method presented here.
引用
收藏
页码：77 / 93
页数：17
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