**Shefaa M. N. Jasim and Ghada H. Ibraheem**

Department of Mathematics, College of Education for Pure Sciences (Ibn AL-Haitham), University of Baghdad

Received:
July 5, 2022

Accepted:
October 11, 2022

Publication Date:
December 14, 2022

* ***Copyright **The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202309_26(9).0013

In conducting this research, the operational matrices methodology was applied. Bernstein and Legendre’s operational matrices have been used to solve the Bagley-Torvik equation. The Liouville-Caputo idea characterizes fractional derivative. The goal of these methods is to turn problems into a system of algebraic equations so that the unknowns may be easily found. Mathematica® 12 program was used to get the outcomes. Examples are provided to illustrate the efficacy of the two suggested techniques. Both approaches are successful, as shown by positive comparisons between the approximate and exact solutions to the problems.

Keywords:
Operational matrix, Bernstein polynomials, Legendre polynomials, Bagley-Torvik equations.

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