An Operational Matrix of Fractional Derivatives of Laguerre Polynomials

Abstract

In this paper, we derive the Laguerre operational matrix (LOM) of fractional derivatives, which is applied together with the spectral tau method for numerical solution of general linear multi-term fractional differential equations (FDEs) on the half line. A new approach implementing Laguerre operational matrix in combination with the Laguerre collocation technique is introduced for solving nonlinear multi-term FDEs. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, greatly simplifying the problem. The proposed methods are applied for solving linear and nonlinear multi-term FDEs, subject to initial conditions, and the exact solutions are obtained for some tested problems. doi:10.14456/WJST.2014.59

Keywords

• Multi-term fractional differential equations
• nonlinear fractional differential equations
• operational matrix
• Laguerre polynomials
• Tau method
• collocation method