Numerical Approximations for Fractional Differential Equations and Related Topics

The concept of a fractional derivative has fascinated scientists ever since the development of the foundations of differential and integral calculus. In the last few decades there has been a spectacular increase of studies regarding fractional derivatives, due to their numerous new applications in the modelling of many real-life physical phenomena. Our project aims to combine the expertise of the supervisor and the applicant in order to publish new results in the field of fractional differential equations and to strengthen the scientific cooperation between the University of Tartu and the University of Florence. To this end, we plan to construct and justify a novel high-order numerical method for solving wide classes of linear and nonlinear fractional differential equations. We also plan to develop and release a software library implementing this algorithm. We expect to publish the obtained scientific results of the project in at least two scientific papers.