On the (k,s)-Hilfer-Prabhakar Fractional Derivative With Applications to Mathematical Physics - Samraiz, Muhammad; Perveen, Zahida; Rahman, Gauhar; Nisar, Kottakkaran Sooppy; Kumar, Devendra (Frontiers in Physics, 2020)
In this paper we introduce the (k, s)-Hilfer-Prabhakar fractional derivative and discuss its properties. We find the generalized Laplace transform of this newly proposed operator. As an application, we develop the generalized fractional model of the free-electron laser equation, the generalized time-fractional heat equation, and the generalized fractional kinetic equation using the (k, s)-Hilfer-Prabhakar derivative.