A shifted Jacobi-Gauss-Lobatto collocation method for solving nonlinear fractional Langevin equation involving two fractional orders in different intervals

Boundary value problems

Mohammed A Alghamdi¹  Ali H Bhrawy² 

[1] Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: fractional Langevin equation;    three-point boundary conditions;    collocation method;    Jacobi-Gauss-Lobatto quadrature;    shifted Jacobi polynomials;   

DOI  :  10.1186/1687-2770-2012-62

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we develop a Jacobi-Gauss-Lobatto collocation method for solving the nonlinear fractional Langevin equation with three-point boundary conditions. The fractional derivative is described in the Caputo sense. The shifted Jacobi-Gauss-Lobatto points are used as collocation nodes. The main characteristic behind the Jacobi-Gauss-Lobatto collocation approach is that it reduces such a problem to those of solving a system of algebraic equations. This system is written in a compact matrix form. Through several numerical examples, we evaluate the accuracy and performance of the proposed method. The method is easy to implement and yields very accurate results.

【 授权许可】

CC BY