In this article, we use the modified extended direct algebraic method (mEDAM) to explore and analyze the traveling wave phenomena embedded in the quintic conformable Benney-Lin equation (CBLE) that regulates liquid film dynamics. The proposed transformation-based approach developed for nonlinear partial differential equations (PDEs) and fractional PDEs (FPDEs), efficiently produces a plethora of traveling wave solutions for the targeted CBLE, capturing the system's nuanced dynamics. The methodically determined traveling wave solutions are in the form of rational, exponential, hyperbolic and trigonometric functions which include periodic waves, bell-shaped kink waves and signal and double shock waves. To accurately depict the wave phenomena linked to these solutions, we generate 2D, 3D, and contour graphs. These visualizations not only improve understanding of the CBLE model's dynamics, but also provide a detailed way to examine its behavior. Moreover, the use of the proposed techniques contributes to a better understanding of the other FPDEs' distinct characteristics, enhancing our comprehension of their underpinning dynamics.

Null boundary controllability refers to the ability to drive the state of a dynamical system to zero by applying suitable control inputs on the boundary of the domain. This research investigates the sufficient conditions for the null boundary controllability of Atangana-Baleanu (A-B) fractional stochastic differential equations involving fractional Brownian motion (fBm) within Hilbert space. We employ various tools, including fractional analysis, compact semigroup theory, fixed point theorems, and stochastic analysis, to derive the desired results. An example is included to illustrate the application of our findings.