Hilfer-Prabhakar Derivatives and Some Applications

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.

References in corpus (2)

• Fractional Calculus: Integral and Differential Equations of Fractional Order
• The fundamental solution of the space-time fractional diffusion equation

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