Dmytro Sytnyk

Project

Our research was focused on the development of novel analytical and numerical tools for mathematical modeling of fractional phenomena.
Fractional calculus is an emerging field of study that deals with the extension of classical calculus, operating with integrals and ­derivative of integer order, to the case when the order parameter might be non-integer.
In many applications the use of fractional calculus leads to more accurate models than those constructed using ordinary integer calculus. Among such applications are diffusion in porous media, phase transition and separation in mixtures of liquids or polymers, wave propagation and energy dissipation in geology, and dumping and crack propagation in structural mechanics. For certain classes of models, fractional order description is necessary to properly capture the essence of underlying phenomena. This is especially true for transient systems that involve some sort of “memory” effect, e.g., shape-memory ­alloys, self-assembling materials, information processing systems, and financial markets. Usually, such complex systems are modeled with the help of time-dependent fractional ­differential equations that require new tools for analysis and numerical solution. They constitute the main object of our study.