Olaniyi Iyiola, Department of Mathematics and Physical Sciences, California University of Pennsylvania
Efficient Methods for Solving Diffusion-Reaction Systems of Fractional Order Type
Nonlocality and spatial heterogeneity of many practical systems have made fractional differential equations very useful tools in Science and Engineering. However, solving these type of models is computationally demanding. In this talk, I will present an overview of fractional calculus and some of my recent results on solving fractional diffusion-reaction problems. In the first part, I will briefly discuss a novel method of determining the solution and the source function (inverse problem) for a two-parameter fractional diffusion equation. This problem models several physical processes such as the microwave heating and light propagation in photoelectric cells. The second part of my talk will focus on the numerical solution of nonlinear reaction-diffusion fractional models using exponential time differencing. Different approaches to spatial discretization of the reaction-diffusion fractional systems which are very important in reducing computational time will be discussed. Generally, the mechanisms of cell motility and/or the generation of chemical pre-patterns are modeled using ideas of biological pattern formation. Several models for pattern formation have been proposed to explain the regenerative properties of hydra which have been experimentally observed in various transplantations. Invoking the intrinsic properties of fractional calculus is therefore apparent in biological and biochemical systems due to these complexities. I will present some applications of fractional calculus in biological pattern formation. I will conclude the presentation with several open problems in this area and my new area of research in data science.