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This article applied the Riccati-Bernoulli (RB) sub-ODE method in order to get new exact solutions for the long-short-wave interaction (LS) equations. Namely, we obtain deterministic and random solutions, since we consider the proposed method in deterministic and random cases. The RB sub-ODE technique gives the travelling wave solutions in forms of hyperbolic, trigonometric and rational functions. It is shown that the proposed method gives a robust mathematical tool for solving nonlinear wave equations in applied science. Furthermore, some bi-random variables and some random distributions are used in random case corresponding to the LS system. The stability for the obtained solutions in random case is considered. In addition, there is a display of several numerical simulations, which helps to understand the physical phenomena of these soliton wave solutions. ARTICLE HISTORY

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In this work, the conformable fractional derivative with the unified solver method are used in the suitable cases to extract new solutions for space-time stochastic fractional nonlinear Schrödinger equation (NLSE) with spatiotemporal dispersion. Namely, some new stochastic solutions with physical parameters for this equation are constructed via exponential distribution. Exponential distribution is employed to clarify the dispersion random effect. The expectation (mean) of stochastic solutions are depicted to exhibit the effect of random parameters on the solutions of space-time stochastic fractional NLSE with spatiotemporal dispersion. These results are highly applicable to develop new theories of plasma physics, industrial studies, biomedical problems, condense matter physics and optical fibers. Simulations are performed by using Maple software. According to the presented results, the proposed technique can be applied for other fractional models arising in natural sciences. Definition 1.1 [31] Given a function ( ) j ¥   : 0, , hence the conformable fraction derivative of j of order α isRECEIVED