To Be Presented in the 11th Asian Technology Conference in Mathematics
December 12-16, 2006, Hong Kong SAR, China

A Numerical Solution for Fractional Differential Equations

Hossein Parsian
Department of physics
University of Bu Ali Sina
Iran

Abstract

In this paper, we present a numerical solution for solving fractional differential equation of order |W ( n −1 < |W < n and n in N ). This numerical solution is based on expansion over wavelets. Wavelets constitute a family of function that constructed from dilation and translation of a single function. The mother function of Legendre wavelet is Legendre function. Legendre wavelets are defined over the interval [0,1]. In recent years, Legendre wavelets are used for solving differential equations, Integral equations and variational problems. In this research work, we present an operational matrix for fractional derivative. The operational matrix develops the Legendre wavelets formalism to fractional calculus. We formulate this problem in terms of left Riemann-Liouville fractional derivative. Several examples demonstrate the validity of this operational matrix.

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