Multiwave solutions of fractional 4th and 5th order Burgers equations

Abstract

Fractional 4th and 5th order Burgers equations were studied by improving the generalized Exp-functionmethod. The chief aim here was to discuss single-wave, double-wave, three-wave, and four-wave solutions for thespace-time fractional (STF), time-fractional (TF), and space-fractional (SF) 4th and 5th order Burgers equations. Thearbitrariness of the fractional orders allows much richer structures. It was observed that the wave amplitude of STF andSF Burgers equations is directly proportional to the noninteger derivative order, but the wave amplitude of TF Burgersequations 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 waveshape can be modi ed based on the noninteger derivative order without changing the properties of the medium.