The aim of this study is to establish an efficient method for exploring the fractional dynamics of fourth-order parabolic partial differential equations. The generalized bivariate homotopy perturbation method is suggested to determine expansion solutions for the considered mod-els. This scheme decomposes non-linearity using He’s polynomials. It is applied within the non-local fractional framework of Liouville-Caputo sense. The impact of fractional phenomena is briefly described. A comparative analysis of the suggested scheme is presented through graphical and tabular illustrations. Error analysis, based on the evaluation of absolute error, demonstrates the high precision, authenticity, and superiority of the suggested scheme. The existence and uniqueness of continuous solutions are shown for the fractional variants of Cauchy problems. The semi-analytic results obtained from the suggested scheme effectively capture the wave dynamics of physical systems across various physical parameters. The proposed algorithm does not rely on the availability of an exact solution to demonstrate its efficacy.