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Application of Müntz-Legendre polynomials for solving the Bagley-Torvik equation in a large interval. (English) Zbl 1412.34040

Summary: 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 Müntz-Legendre polynomials. For this purpose, first, we derive an operational matrix of fractional integration based on Müntz-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 Müntz-Legendre coefficients are computed. The accuracy and performance of the proposed method are demonstrated by some numerical examples.

MSC:

34A08 Fractional ordinary differential equations
41A10 Approximation by polynomials
34A45 Theoretical approximation of solutions to ordinary differential equations
34A30 Linear ordinary differential equations and systems
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