Numerical solution for solving fractional differential equations using shifted Chebyshev wavelet

Abstract EN

In this paper, we are interested to develop a numerical method based on the Chebyshev wavelets for solving fractional order diferential equations (FDEs).

As a result of the presentation of Chebyshev wavelets, we highlight the operational matrix of the fractional order derivative through wavelet-polynomial matrix transformation which was utilized together with spectral and collocation methods to reduce the linear FDEs, to a system of algebraic equations.

This method is a more simple technique of obtaining the operational matrix with straight forward applicability to the FDEs .

The main characteristic behind the approach using this technique is that only a small number of shifted Chebyshev polynomials is needed to obtain a satisfactory results.

Illustrative examples reveal that the present method is very effective and convenient for linear FDEs.