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.
Hilfer-Prabhakar Derivatives and Some Applications
POLITO, Federico;
2014-01-01
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. 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.
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