Approximate analytical solution of the space-and time-fractional Burgers equations

This paper presents approximate analytical solutions for the generalized fractional time-space Burgers equations. The time-and space-fractional derivatives are considered in the Caputo sense. The application of variational iteration method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of the spaceand time-fractional Burgers equation. The solutions of our model equation are calculated in the form of convergent series with easily computable components. Two examples are presented to show the application of the present technique. The effect of varying the order of the time-and space-fractional derivatives on the behaviour of solutions has been investigated.