Application of Fractional calculus in Mathematical Biology

The fractional calculus is widely used to formulate model in epidemiology. These models are not limited to population studies but also to the study of cells, tissues etc. The complexity of all living systems is expressed in the structure and function of each cell and tissue. Thus, the biological functions of cardiac muscle, articular cartilage and the spinal cord, for example, are embedded in the three-dimensional structure of each tissue’s cells, extracellular matrix, and overall anatomical organization. In the heart, tight electrical contacts between cardiac cells ensure that the pacemaker signals are distributed sequentially to the atria and ventricles; in the knee, the multiple layers within hyaline cartilage distribute transient loads by the rapid movement of ions and water; while in the axons of the spinal cord, sensory input and reflexes are expressed via electrical signals – action potentials – that are directed through complex neural networks. The physiologist seeks to understand such complex behavior by gently probing the cell and tissue environment and by developing mathematical models that describe the resulting perturbations (e.g., ECG changes, gait variation, evoked potential latency). These mathematical models are typically constructed using linear and nonlinear differential equations (LDE) and provide a means for predicting the time variation of the experimentally measured fields, forces and flows that regulate biomechanical, neural and hormonal processes.