Abstract
Fractional 4th and 5th order Burgers equations were studied by improving the generalized Exp-function method. The chief aim here was to discuss single-wave, double-wave, three-wave, and four-wave solutions for the space-time fractional (STF), time-fractional (TF), and space-fractional (SF) 4th and 5th order Burgers equations. The arbitrariness of the fractional orders allows much richer structures. It was observed that the wave amplitude of STF and SF Burgers equations is directly proportional to the noninteger derivative order, but the wave amplitude of TF Burgers equations is inversely proportional to the noninteger derivative order. From the graphical study of the obtained solution, a change in the noninteger derivative order value affects soliton behavior in a fundamental way. Therefore, the wave shape can be modified based on the noninteger derivative order without changing the properties of the medium.