On Mittag-Leffler-type functions in fractional evolution processes

We review a variety of fractional evolution processes (so defined being governed by equations of fractional order), whose solutions turn out to be related to Mittag-Leffler-type functions. The chosen equations are the simplest of the fractional calculus and include the Abel integral equations of the second kind, which are relevant in typical inverse problems, and the fractional differential equations, which govern generalized relaxation and oscillation phenomena.