An Approximate Solution of the Time-Fractional Two-Mode Coupled Burgers Equation

In this paper, we consider the time-fractional two-mode coupled Burgers equation with the Caputo fractional derivative. A modified homotopy perturbation method coupled with Laplace transform (He-Laplace method) is applied to find its approximate analytical solution. The method is to decompose the equation into a series of linear equations, which can be effectively and easily solved by the Laplace transform. The solution process is illustrated step by step, and the results show that the present method is extremely powerful for fractional differential equations.

Automated summary

In this paper, the time-fractional two-mode coupled Burgers equation with the Caputo fractional derivative is considered, and the He-Laplace method is applied to find its approximate analytical solution. The method decomposes the equation into a series of linear equations, which can be easily solved through Laplace transform. The step-by-step illustration of the solution process demonstrates the method's effectiveness for fractional differential equations.