Computational method based on Bernstein operational matrices for multi-order fractional differential equations

In this paper, the Bernstein operational matrices are used to obtain solutions of multi-order fractional differential equations. In this regard we present a theorem which can reduce the nonlinear fractional differential equations to a system of algebraic equations. The fractional derivative considered here is in the Caputo sense. Finally, we give several examples by using the proposed method. These results are then compared with the results obtained by using Adomian decomposition method, differential transform method and the generalized block pulse operational matrix method. We conclude that our results compare well with the results of other methods and the efficiency and accuracy of the proposed method is very good.