On 21 February at 14:15 Mikk Vikerpuur will defend his doctoral thesis „Numerical solution of fractional differential equations”.
Professor Arvet Pedas
Professor Ewa Weinmüller dr, Vienna University of Technology
Professor Neville J Ford, University of Chester
The concept of a fractional derivative can be traced back to the end of the seventeenth century, the time when Newton and Leibniz developed the foundations of differential and integral calculus. Despite this, for a long time, considerations regarding fractional derivatives were purely theoretical treatments for which there were no serious practical applications. It is only during the last decades that there has been a spectacular increase of studies regarding fractional derivatives and differential equations with such deri- vatives, mainly because of new applications of fractional derivatives in several fields of applied science. However, when working with problems stemming from real-world applications, it is only rarely possible to find the exact solution of a given fractional differential equation, and even if such an analytic solution is available, it is typically too complicated to be used in practice. Therefore numerical methods specialized for solving fractional differential equations are required. In the present thesis the regularity pro- perties of the exact solutions of a wide class of fractional differential and integro-diffe- rential equations are investigated. Based on the obtained regularity properties, the numerical solution of the problem is discussed, the convergence of proposed algorithms is proven and their global convergence estimates are derived. The obtained theoretical results are supported by many numerical experiments with various test problems.