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In the present paper, a numerical technique for solving the fractional Bagley-Torvik equation with homogeneous boundary conditions is investigated. The nonhomogeneous conditions were transformed to homogeneous ones. The technique is based on applying the tau method to reduce the solution of fractional Bagley-Torvik equation for a system of algebraic equations. The latter equations may be solved using the Gaussian elimination procedure. The convergence and error analysis of the generalized Fibonacci basis are discussed in detail. Some explanatory examples are provided to assert the validity, accuracy and applicability of this technique.

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