A novel exploration of the relationship between coarseningCoarsening annealingAnnealing and the moving boundary problemMoving Boundary Problems (MBP) approach is attempted, with a particular emphasis on diffusion. Stefan’s solution and non-integer exponents in the power law of interface versus time are simulated. The research delves into the complex dynamics of phase transformations, specifically the process of coarseningCoarsening annealingAnnealing, in effectively modeling the moving boundary problemMoving Boundary Problems (MBP). The role of diffusion in these transformations is explored, elucidating how atomic mobility influences the coarseningCoarsening process. A significant focus of this study is the investigation of non-integer exponents in the power law of interface versus time. This aspect challenges traditional models and provides a more nuanced understanding of phase transformations. It is demonstrated through the enthalpy formulation of the Moving Boundary ProblemMoving Boundary Problems (MBP) (MBPMoving Boundary Problems (MBP)) that the interface aligns closely with the Stefan solution. However, non-integer exponents can accurately model interfacial dynamics over a larger time, offering new insights into the coarseningCoarsening process.