An efficient approximate method for solving linear fractional Klein–Gordon equation based on the generalized Laguerre polynomials

Abstract

In this paper, a new approximate formula of the fractional derivative is derived. The proposed formula is based on the generalized Laguerre polynomials. Global approximations to functions defined on a semi-infinite interval are constructed. The fractional derivatives are presented in terms of Caputo sense. Special attention is given to study the error and the convergence analysis of the proposed formula. A new spectral Laguerre collocation method is presented for solving linear fractional Klein–Gordon equation (LFKGE). The properties of Laguerre polynomials are utilized to reduce LFKGE to a system of ordinary differential equations, which solved using the finite difference method. Numerical results are provided to confirm the theoretical results and the efficiency of the proposed method.

Keywords:

• linear fractional Klein–Gordon equation
• Caputo fractional derivatives
• Laguerre polynomials
• finite difference method
• collocation methods
• error analysis

2000 AMS Subject Classifications :

• 65K10
• 35A15
• 41A99
• 41E20
• 65G99

Additional information

Notes on contributors

M. M. Khader

Current address: Department of Mathematics, Faculty of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi