Solving Nonlinear Fractional Differential Equations by Bernstein Polynomials Operational Matrices

In this paper, we solve nonlinear fractional differential equations by Bernstein polynomials. Firstly, we derive the Bernstein polynomials (BPs) operational matrix for the fractional derivative in the Caputo sense, which has not been undertaken before. This method reduces the problems to a system of algebraic equations. The results obtained are in good agreement with the analytical solutions and the numerical solutions in open literatures. Also, the solutions approach to classical solutions as the order of the fractional derivatives approach to 1.