Numerical solutions of time-fractional Burgers equations A comparison between generalized differential transformation technique and homotopy perturbation method

Purpose - The purpose of this paper is to use the generalized differential transform method (GDTM) and homotopy perturbation method (HPM) for solving time-fractional Burgers and coupled Burgers equations. The fractional derivatives are described in the Caputo sense. Design/methodology/approach - In these schemes, the solutions takes the form of a convergent series. In GDTM, the differential equation and related initial conditions are transformed into a recurrence relation that finally leads to the solution of a system of algebraic equations as coefficients of a power series solution. HPM requires a homotopy with an embedding parameter which is considered as a small parameter. Findings - The paper extends the application and numerical comparison of the GDTM and HPM to obtain analytic and approximate solutions to the time-fractional Burgers and coupled Burgers equations. Research limitations/implications - Burgers and coupled Burgers equations with time-fractional derivative used. Practical implications - The implications include traffic flow, acoustic transmission, shocks, boundary layer, the steepening of the waves and fluids, thermal radiation, chemical reaction, gas dynamics and many other phenomena. Originality/value - The numerical results demonstrate the significant features, efficiency and reliability of the two approaches. The results show that HPM is more promising, convenient, and computationally attractive than GDTM.