The existence and forms of solutions for some Fermat-type differential-difference equations

The main aim of this article is to investigate the existence and the forms of solutions for several complex differential-difference equations of Fermat-type. Our results about the existence and the forms of solutions for these Fermat type equations are great improvement of the previous theorems given by Liu, Yang, Cao, Zhang. Moreover, it is a very satisfactory fact that in some examples explicit solutions are given.