AUTHORS: Vijay Saw, Sushil Kumar

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ABSTRACT: In this paper, we propose numerical scheme for solving two point fractional Bagley-Torvik equation (FBTE). The scheme is based on collocation and using shifted Chebyshev polynomials of the second kind (SCPSK) orthogonal basis functions. In this case, we replace an integer order derivatives by fractional order derivatives in Caputo sense. By using the properties of SCPSK to reduce fractional Bagley-Torvik equation into system of algebraic equations, which can be solved by iteration method. The error analysis and error bounds are discussed. The validation of the present algorithm is tested through number of examples. All computational results are done in Matlab.

KEYWORDS: Caputo fractional derivative, Chebyshev polynomials of the second kind, Collocation method, Fractional Bagley-Torvik equation, Convergence analysis

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