In this article, we obtain numerical solutions of Bagely-Torvik and a class of fractional oscillation equations by using a numerical method based on Hosoya and Clique polynomials. The fractional derivative is in the Coputo sense. In this method, rst we convert the given fractional order di erential equations to corresponding fractional integral equations, and then we use the Rayleigh-Ritz method and collocation points to transform the fractional integral equation into a system of algebraic equations. Finally, we gain a numerical result by solving the consequent algebraic system
