Fundamental analysis of the time fractional coupled Burgers-type equations

Abstract

Fractional differential equations play an essential role in describing the shallow water wave phenomena. In this article, we discussed the coupled Burgers-type equations in the sense of the fractional derivative of Riemann-Liouville. In return, a series of new results of this considered models, were obtained. In the first place, the formulation of the time fractional coupled Burgers-type equations by applying the Euler-Lagrange variational technology, was carried out. Then, the symmetry and one-parameter group of point transformations of this researched goals through the symmetry analysis scheme, were obtained. Subsequently, the time fractional coupled Burgers-type equations can be reduced into the fractional ordinary differential equations with the help of the Erdélyi-Kober fractional differential/integral operators. Next, the approximate solution and convergence analysis, were considered. At the same time, the stability analysis of the solitary wave, was also studied. Lastly, conservation laws of this discussed equations by using a new conservation theorem and nonlinear self-adjointness, were found. The series of results obtained above can provide strong support for us to reveal the mystery of the equation.