Abstract
In this paper, a new numerical method for the approximate solution of the Bagley–Torvik equation which belongs to a class of fractional differential equations is proposed. The basic idea of this method is to obtain the approximate solution in a generalized form of the Muntz–Legendre polynomials. For this purpose, first, we derive an operational matrix of fractional integration based on Muntz–Legendre polynomials. Then, by using this matrix and collocation method, the Bagley–Torvik equation is reduced into a system of algebraic equations. Hence, by solving this system, the unknown Muntz–Legendre coefficients are computed. The accuracy and performance of the proposed method are demonstrated by some numerical examples.
Published Version
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