**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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