Refaad for Studies, Research and Developement
Numerical Solution for Solving Fractional Diﬀerential Equations using Shifted Chebyshev Wavelet
25199269 (Print)
25199277 (Online)
Volume 3
Issue 2
2017

0
Numerical Solution for Solving Fractional Diﬀerential Equations using Shifted Chebyshev Wavelet
102
111
English
Mohamed Elarabi Benattia Laboratory of Mathematics and its Applications (LAMAP) University of Oran 1, Ahmed Ben Bella mohamed.benattia74@yahoo.com
Belghaba KacemLaboratory of Mathematics and its Applications (LAMAP) University of Oran 1, Ahmed Ben Bella belghaba@yahoo.fr
In this paper, we are interested to develop a numerical method based on the Chebyshev wavelets for solving fractional order diﬀerential equations (FDEs). As a result of the presentation of Chebyshev wavelets, we highlight the operational matrix of the fractional order derivative through waveletpolynomial 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.
Operational matrix; shifted Chebyshev wavelet; fractional derivatives; shifted Chebyshev polynomials; Caputo fractional derivative
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