The Classification of Traveling Wave Solutions to Space-Time Fractional Resonance Nonlinear Schrödinger Type Equation with a Special Kind of Fractional Derivative

In this paper, the classification of single traveling wave solutions to a special kind of space-time fractional Schrödinger type equation with high-order nonlinearities is obtained by the complete discrimination system for polynomial method, where the fractional derivative is defined by Atangana’s conformable definition. The descriptions of the method and the fractional derivative are given, and the concrete procedure of the method is also presented in the paper. Especially, some new solutions such as hyperelliptic functions solution could be found and all the existing results about traveling wave solutions to the equation could also be seen. Moreover, concrete examples indicate that all the solutions obtained in the paper can be realized.