To Be Presented in the 11th Asian Technology Conference in Mathematics December 12-16, 2006, Hong Kong SAR, China |
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## A Numerical Solution for Fractional Differential EquationsHossein ParsianDepartment of physics University of Bu Ali Sina Iran
## Abstract In this paper, we present a numerical solution for solving fractional
differential equation of order |ˆW ( n −1 < |ˆW < 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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