The Operational Matrices Methods For Solving The Fractional Bagley-Torvik Equations

Abstract

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