Approximate analytical solution of the nonlinear fractional KdV–Burgers equation: A new iterative algorithm

In this paper, explicit and approximate solutions of the nonlinear fractional KdV–Burgers equation with time–space-fractional derivatives are presented and discussed. The solutions of our equation are calculated in the form of rabidly convergent series with easily computable components. The utilized method is a numerical technique based on the generalized Taylor series formula which constructs an analytical solution in the form of a convergent series. Five illustrative applications are given to demonstrate the effectiveness and the leverage of the present method. Graphical results and series formulas are utilized and discussed quantitatively to illustrate the solution. The results reveal that the method is very effective and simple in determination of solution of the fractional KdV–Burgers equation.