A fractional-order Legendre collocation method for solving the Bagley-Torvik equations

Advances in Difference Equations

Syed Tauseef Mohyud-Din¹  Fakhrodin Mohammadi² 

[1] Department of Mathematics, HITEC University, Taxila Cantt, Pakistan;Department of Mathematics, University of Hormozgan, Bandarabbas, Iran

关键词: Bagley-Torvik equations;    Riemann-Liouville fractional integration;    fractional-order Legendre polynomials;    operational matrix;    collocation method;    26A33;    34A08;    65N35;   

DOI  :  10.1186/s13662-016-0989-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, a numerical method based on the fractional-order shifted Legendre polynomials (FSLPs) and their operational matrix of fractional integration is introduced for solving the fractional Bagley-Torvik equations. The main advantage of the presented method is that it can reduce a solution of the initial and boundary value problems for the fractional Bagley-Torvik differential equations to a system of algebraic equations. In order to confirm the efficiency and superiority of the presented method, some numerical examples are provided and a comparison is presented between the obtained results and those results achieved from other existing methods in the literature.

【 授权许可】

CC BY