Numerical study of time-fractional fourth-order differential equations with variable coefficients

In this article, we study numerical solutions of time-fractional fourth-order partial differential equations with variable coefficients by introducing the fractional derivative in the sense of Caputo. We implement reliable series solution techniques namely Adomian decomposition method (ADM) and He’s variational iteration method (HVIM). Some applications are presented to highlight the significant features of these techniques. The comparison shows that the solutions obtained are in good agreement with each other and with their respective exact solutions. Some of these types of differential equations arise practically in the theory of transverse vibrations.