The fractional-stochastic Fokas-Lenells equation (FSFLE) in the Stratonovich sense is taken into account here. The modified mapping method is used to generate new trigonometric, hyperbolic, elliptic and rational stochastic fractional solutions. Because the Fokas-Lenells equation has many implementations in telecommunication modes, complex system theory, quantum field theory, and quantum mechanics, the obtained solutions can be employed to describe a wide range of exciting physical phenomena. We plot several 2D and 3D diagrams to demonstrate how multiplicative noise and fractional derivatives affect the analytical solutions of the FSFLE. Also, we show how multiplicative noise at zero stabilizes FSFLE solutions.

Here, we consider the stochastic Kakutani–Matsuuchi model (SKMM) perturbed by multiplicative noise in the Itô sense. This model describes the behavior of these waves as they propagate through a stratified fluid medium, such as the Earth's atmosphere or ocean. Internal gravity waves are generated by disturbances in the density or temperature of the fluid and can play a significant role in transporting energy and momentum throughout the system. By applying two different techniques, namely the extended tanh function method and the mapping method, we obtain new periodic soliton, dark soliton, bright soliton, anti-Kink soliton and Kink soliton solutions for SKMM. Because the Kakutani–Matsuuchi model is important in studying internal gravity waves in the atmosphere and oceans, the solutions of the SKMM are beneficial in understanding several fascinating scientific phenomena. Using MATLAB, we exhibit several 2D and 3D graphs that illustrate the impact of the noise on the solutions of SKMM.