Mathematical Analysis

Modeling of complex biological phenomena has become fashionable over the past two decades, as the computing power required to analyze such models has become available. On the other side, non-local calculus has gained significance owing to its applications in various biological and physical phenomena. The theory of non-local calculus has to be developed in order to better analyse and understand these physical and biological phenomena. Dr. Adnan Khan has been working in this area, from modeling dynamics of proteins to the mathematical study of epidemics. Being the basic building blocks of life, we would like to understand how proteins move, this is a computationally intensive task using brute force techniques; Dr. Khan is interested in developing models which are simpler (easier to compute), yet capture all the essential dynamics. Another area of his research has been the modeling of epidemics, and using control theory to suggest measures for their management. Dr Zaidi has been working on developing techniques for solving non-local (functional) ordinary and partial differential equations. These equations arise in size structured cell growth models. Cell cohorts growing and dividing simultaneously are usually structured on size. The latter introduces the non-local effect which creates complexity."