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Numerical Solution for Solving Fractional Differential Equations using Shifted Chebyshev Wavelet

Volume 3, Issue 2, Article 3 - 2017

Authors: Mohamed Elarabi Benattia ;Belghaba Kacem

Copyright © 2017 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

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 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.

How To Cite This Article

@article{Elarabi_Benattia_2017, doi = {10.31559/glm2016.3.2.3}, url = {https://doi.org/10.31559%2Fglm2016.3.2.3}, year = 2017, month = {oct}, publisher = {Refaad for Studies and Research}, volume = {3}, number = {2}, author = {Mohamed Elarabi Benattia and Belghaba Kacem}, title = {Numerical Solution for Solving Fractional Differential Equations using Shifted Chebyshev Wavelet}, journal = {General Letters in Mathematics} }
Elarabi Benattia, M., & Kacem, B. (2017). Numerical Solution for Solving Fractional Differential Equations using Shifted Chebyshev Wavelet. General Letters in Mathematics, 3(2). doi:10.31559/glm2016.3.2.3
[1]M. Elarabi Benattia and B. Kacem, “Numerical Solution for Solving Fractional Differential Equations using Shifted Chebyshev Wavelet,” General Letters in Mathematics, vol. 3, no. 2, Oct. 2017.
1. Elarabi Benattia M, Kacem B. Numerical Solution for Solving Fractional Differential Equations using Shifted Chebyshev Wavelet. General Letters in Mathematics [Internet]. Refaad for Studies and Research; 2017 Oct 1;3(2). Available from: http://dx.doi.org/10.31559/glm2016.3.2.3