Non-perturbative analytical solutions of the space- and time-fractional Burgers equations

Non-perturbative analytical solutions for the generalized Burgers equation with time- and space-fractional derivatives of order α and β, 0 < α, β ⩽ 1, are derived using Adomian decomposition method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed.