IJPAM: Volume 74, No. 3 (2012)

THE APPROXIMATE AND EXACT SOLUTIONS OF
THE FRACTIONAL-ORDER DELAY DIFFERENTIAL
EQUATIONS USING LEGENDRE
SEUDOSPECTRAL METHOD

M.M. Khader$^1$, A.S. Hendy$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Benha University
Benha, EGYPT


Abstract. Fractional differential equations have recently been applied in various area of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The method is based upon Legendre approximations. The properties of Legendre polynomials are utilized to reduce FDDEs to linear or nonlinear system of algebraic equations. Numerical simulation with the exact solutions of FDDEs is presented.

Received: April 30, 2011

AMS Subject Classification: 34A08, 34K37

Key Words and Phrases: fractional delay differential equations, Legendre polynomials, Caputo fractional derivatives

Download paper from here.


Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 74
Issue: 3