  The Prabhakar function (namely, a three parameter Mittag-Leffler function) is
investigated. This function plays a fundamental role in the description of the
anomalous dielectric properties in disordered materials and heterogeneous
systems manifesting simultaneous nonlocality and nonlinearity and, more
generally, in models of Havriliak-Negami type. After reviewing some of the main
properties of the function, the asymptotic expansion for large arguments is
investigated in the whole complex plane and, with major emphasis, along the
negative semi-axis. Fractional integral and derivative operators of Prabhakar
type are hence considered and some nonlinear heat conduction equations with
memory involving Prabhakar derivatives are studied.
