Soliton solutions of the space–time fractional nonlocal nonlinear Schrödinger equation

In this paper, the space–time fractional nonlocal nonlinear Schrödinger equations under Jumarie modified Riemann–Liouville derivative is studied. The soliton solutions are formally derived by using the extended tanh method of fractional Riccati subequation and the ansatz method combined with the Hermite–Gaussian function and Mittag-Leffler function. Different types of solutions are obtained and the necessary conditions for the existence of solutions are given. With the help of Maple, we plot figures exhibit that solitons are forming as fractional order λ increasing, and also, we noticed that at different order n of the Hermite–Gaussian function Hn(y), mainly affects the amplitude of soliton. Furthermore, we have discussed the new soliton solutions in the fractional case. It is of great significance to understand complex physical phenomena described by fractional nonlocal nonlinear equations.