© 2022The current analysis employs the improved F-expansion, modified extended tanh, exponential rational function, and (g′)−expansion procedures to find a divergent collection of the fractional Liouville equation's exact solutions in the context of beta-derivative. Also, we have given the graphical representations of the obtained results. These plots are useful in describing the dynamic characteristics of the solutions. The investigated equation is very essential in studying the mechanics of water waves and atmospheric predictability. Therefore, our techniques provide a great help in investigating various nonlinear models formulated in the contexts of fractional derivatives arising from oceanography and mathematical physics.