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. Furthermore, we show some applications of these generalized Hilfer–Prabhakar derivatives in classical equations of mathemati...

Full description

Saved in:

Bibliographic Details
Published in:	Applied mathematics and computation Vol. 242; pp. 576 - 589
Main Authors:	Garra, Roberto, Gorenflo, Rudolf, Polito, Federico, Tomovski, Živorad
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-09-2014
Subjects:	Generalized Poisson processes Hilfer–Prabhakar derivatives Mittag–Leffler functions Prabhakar integrals Prabhakar integrals Hilfer–Prabhakar derivatives Generalized Poisson processes Mittag–Leffler functions
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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. Furthermore, we show some applications of these generalized Hilfer–Prabhakar derivatives in classical equations of mathematical physics such as the heat and the free electron laser equations, and in difference–differential equations governing the dynamics of generalized renewal stochastic processes.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2014.05.129