Anomalous Subdiffusive Behavior of Cytosolic Calcium

In this chapter, we investigate calcium signaling in cardiac myocytes. Calcium is a critical regulator of cardiac myocyte functions. Here, we develop a mathematical model to describe the calcium transients in cardiac myocytes. Since diffusion is a basic transport process involved in the evolution of many non-equilibrium systems toward equilibrium, in this chapter on the basis of the concept of anomalous diffusion, a mathematical model is proposed to characterize the anomalous subdiffusion of cytosolic calcium incorporating the Caputo fractional operator and the fractal derivative with respect to time and space variables, respectively. The model with the incorporation of conformable derivative (which is a combination of the Caputo and proportional derivative) with respect to the time variable and fractal derivative with respect to the space variable is also presented here. The Crank–Nicolson finite difference scheme is applied to obtain the solution, and further numerical simulation is done for various fractal and fractional orders.