Introduction to fractional calculus and some applications

The idea of differential calculus of fractional order is as old as the classical concepts of differentiation and integration that came up in the 17th century. However, it took some time until efforts were made to establish an exhaustive theory of fractional calculus - the first book specifically dedicated to that topic only appeared in 1974.

Until recent times, fractional calculus was considered as a mathematical theory without applications, but in the last decades there has been a growth of research activities on the application of fractional calculus to diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems and finance and economics.

The talk aims to give an introduction to basic definitions and properties of fractional calculus and present two examples of application: Firstly, anomalous diffusion as one of the first fields where fractional differentiation was used, and secondly, a model of an electric circuit as an illustration of dynamical systems of non-integer order.