Generalised fractional calculus: probabilistic and analytic points of view

In the main part of the talk I shall give an overview of the generalised fractional calculus giving glimpses of its origin from different perspectives: probability, functional analysis, pseudo-differential equations. At the end I plan to give a brief account of recent developments including equations with distributed (variable) fractional derivatives, fractional kinetic equations, scaling limits of Léy walks and the rates of convergence of CTRWs (continuous time random walks) to fractional evolutions.