Hilfer-Prabhakar Derivatives and Some Applications
Probability
2014-06-30 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1401.6668,
title = {Hilfer-Prabhakar Derivatives and Some Applications},
author = {Roberto Garra and Rudolf Gorenflo and Federico Polito and Zivorad Tomovski},
journal= {arXiv preprint arXiv:1401.6668},
year = {2014}
}