Symmetry group analysis of several coupled fractional partial differential equations

Abstract

Under investigations were several coupled time–space fractional integrable equations which are called the (1+1)-dimensional KdV-type equations, the (2+1)-dimensional Burgers equations and the (3+1)-dimensional unsteady Euler equations of gas dynamics. In this article, these above considered time–space fractional models through the symmetry analysis approach were explored. As the most basic results, symmetries of these researched equations, were obtained. With the help of the multiple-parameters Erdélyi-Kober fractional operators, they can be reduced into lower dimensional systems. We noticed that this reduction process was somewhat different from the integer case. Besides, we also obtained the explicit power series solution and analyze the convergence to it. By considering the new fractional conservation theorem, conserved quantity of time and space of these time–space fractional systems, were also obtained.