This extensive review explores the numerous functions of fractional calculus in modelling of advanced materials, with a focus on nonlocal motion, fracture cases, diffusion in porous media, heat transfer, and viscosity in particular. This helps explain phenomena such as reactive transport in porous media, heterogeneous sub diffusion, and diffusion processes in irregularly shaped blocks. For fracture media and porous materials to be continuum mechanics, as well as explain linear and nonlinear viscoelastic behaviour, research finds several examples of using different derivatives of fractional calculation to predict her Covers usage, dynamic processes in fractured materials, and thermodynamic concepts. Although the work provides a comprehensive survey of the application of fractional computation to many material situations, further research on computational techniques, theoretical constraints, and empirical validation may increase the breadth and utility of these models.