The approximate solution of higher-order of fractional differential equations using collocation method based on Chebyshev polynomials of third kind
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초록
In this paper, the collocation method for the approximate solution of higher order multiterm fractional differential equations (FDEs) in terms of Chebyshev polynomials. The multi-term FDEs and its initial or boundary conditions are transformed into equations, which correspond to a system of algebraic equations with unknown Chebyshev coefficients. The solution of this system yields the Chebyshev coefficients of the solution formula. Several numerical examples, such as Cauchy and Bagley-Torvik fractional differential equations are provided to confirm the accuracy and the effectiveness of the proposed method. Numerical simulation with the exact solution of FDEs is presented. The graph and approximate solution are calculated in MATLAB.
Abstract
In this paper, the collocation method for the approximate solution of higher order multiterm fractional differential equations (FDEs) in terms of Chebyshev polynomials. The multi-term FDEs and its initial or boundary conditions are transformed into equations, which correspond to a system of algebraic equations with unknown Chebyshev coefficients. The solution of this system yields the Chebyshev coefficients of the solution formula. Several numerical examples, such as Cauchy and Bagley-Torvik fractional differential equations are provided to confirm the accuracy and the effectiveness of the proposed method. Numerical simulation with the exact solution of FDEs is presented. The graph and approximate solution are calculated in MATLAB.
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