Bernoulli Operational Matrix of Fractional Derivative for Solution of Fractional Differential Equations

Volume 5, Issue 1, Article 5 - 2018

Authors: Rachid Belgacem;Ahmed Bokhari;Abdessamad Amir

Copyright © 2018 . 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

The aim of this paper is to present a numerical method based on Bernoulli polynomials for numerical solutions of fractional differential equations(FDEs). The Bernoulli operational matrix of fractional derivatives[31] is derived and used together with tau and collocation methods to reduce the FDEs to a system of algebraic equations. Hence, the solutions obtained using this method give good approximations. Illustrative examples are included to demonstrate the validity and applicability of the proposed method.

How To Cite This Article

@article{Belgacem_2018, doi = {10.31559/glm2018.5.1.5}, url = {https://doi.org/10.31559%2Fglm2018.5.1.5}, year = 2018, month = {aug}, publisher = {Refaad for Studies and Research}, volume = {5}, number = {1}, pages = {32--46}, author = {Rachid Belgacem and Ahmed Bokhari and Abdessamad Amir}, title = {Bernoulli Operational Matrix of Fractional Derivative for Solution of Fractional Differential Equations}, journal = {General Letters in Mathematics} }
Belgacem, R., Bokhari, A., & Amir, A. (2018). Bernoulli Operational Matrix of Fractional Derivative for Solution of Fractional Differential Equations. General Letters in Mathematics, 5(1), 32–46. doi:10.31559/glm2018.5.1.5
[1]R. Belgacem, A. Bokhari, and A. Amir, “Bernoulli Operational Matrix of Fractional Derivative for Solution of Fractional Differential Equations,” General Letters in Mathematics, vol. 5, no. 1, pp. 32–46, Aug. 2018.
Belgacem, Rachid, Ahmed Bokhari, and Abdessamad Amir. “Bernoulli Operational Matrix of Fractional Derivative for Solution of Fractional Differential Equations.” General Letters in Mathematics 5, no. 1 (August 2018): 32–46. doi:10.31559/glm2018.5.1.5.