Fluorescence recovery after photobleaching (FRAP) is a laser microscopy technique extensively used to determine kinetic properties of cells using fluorophores. FRAP is based on irreversibly bleaching a set of proteins tagged with green fluorescent protein (GFP) in a region of interest and monitoring the recovery in fluorescence due to diffusion of surrounding intact probes into the bleached spot. FRAP is being widely used in many areas of biology to measure molecular transport and diffusion in comparison with mathematical models derived for specific domains. This study focused on deriving mathematical models of FRAP for various geometries and conditions depending on their locations in the cell, creating a database, and constructing a mathematical model with the help of MATLAB. FRAP models for pure diffusion for various geometries in 1~2 spatial dimensions with different boundary conditions, which are applicable to both conventional and confocal FRAP, was considered. For a circular bleaching spot, the geometries considered were infinite line, finite interval, a circle, infinite plane, sphere, and infinite three-dimensional space for reflective and restrictive boundary conditions if applicable. Finally, future directions are proposed to focus on interesting ways to apply this new model in vivo.