Organized into four chapters, the book introduces fractional calculus and is devoted to understanding the receptor activation by the ligand, that is Thrombin via fractional model incorporating the Caputo-Fabrizio fractional operator. It studies the calcium profile in red blood cells with the help of the advection-diffusion equation. The book further studies the process of buffering, aiding  the lowering of the calcium concentration in the cytosol, which rises due to calcium influx from extracellular space and intracellular storage. It explains the concept of anomalous diffusion-a mathematical model is proposed to characterize the anomalous subdiffusion of cytosolic calcium.