The new stochastic solutions for the fractional stochastic (3+1)-model of fluid with gas bubbles

This study investigates the fractional (3 + 1)-dimensional equation for fluids with gas bubbles through conformable fractional operator, incorporating a noise term through the modified Sardar sub-equation method. This equation describes nonlinear wave propagation in compressible fluids containing distributed gas microbubbles, which is ubiquitous in biological tissues, petroleum engineering, acoustics, and fluid-structure interactions. The fractional derivative incorporates memory effects and anomalous dispersion, enhancing the model’s accuracy in reflecting real-world phenomena. The mathematical system is transformed into a nonlinear ordinary differential equation by applying a complex traveling wave transformation. We provide some innovative stochastic solutions through free physical parameters for the suggested model via Brownian motion process. The novel stochastic solutions investigated how noise affects frequencies in nonlinear systems such as biomedical ultrasonography, nuclear science, fluid-structure interaction, and more. To demonstrate the behavior of the offered stochastic solutions, a variety of profile graphs were created utilizing the Matlab release’s capabilities. The proposed methodology can ultimately be modified for use with a range of other models in applied science.