Auto-Bäcklund transform and exact solutions to local conformable time-fractional viscous Burgers system

The classical Burgers equation is one of important nonlinear models in fluid mechanics, which is often used to describe acoustical waves, electromagnetic waves, etc. This paper generalizes the discussions on the classical Burgers equation to that for the multi-dimensional local conformable time-fractional Burgers system. The corresponding auto-Bäcklund and Hopf-Cole transforms are also obtained. By solving the local fractional linear heat equation, we derive many exact solutions and, to the best of our knowledge, some of them are very new. The impact of the fractional derivative on the solutions is also discussed.