Hilfer-Prabhakar Derivatives and Some Applications
  We present a generalization of Hilfer derivatives in which Riemann--Liouville integrals are replaced by more general Prabhakar integrals. We analyze and discuss its properties. Further, we show some applications of these generalized Hilfer-Prabhakar derivatives in classical equations of mathematical physics, like the heat and the free electron laser equations, and in difference-differential equations governing the dynamics of generalized renewal stochastic processes. 
Roberto Garra, Rudolf Gorenflo, Federico Polito, Zivorad Tomovski
math.PR