An efficient computational method for solving fractional biharmonic equation

In this paper, we first introduce the fractional biharmonic equation and an orthogonal system of basis functions for the space of continuous functions on the interval , generated by the shifted Chebyshev polynomials. Moreover, we propose a computational method based on the operational matrix of fractional derivatives of these basis functions for solving the fractional biharmonic equation. The main characteristic behind this approach is that it reduces the problem under consideration to solving a system of algebraic equations which greatly simplifies the problem. Convergence of the shifted Chebyshev polynomials expansion in two-dimensions is investigated. Also the power of this manageable method is illustrated.