AUTHOR=Samraiz Muhammad , Perveen Zahida , Rahman Gauhar , Nisar Kottakkaran Sooppy , Kumar Devendra 

TITLE=On the (k,s)-Hilfer-Prabhakar Fractional Derivative With Applications to Mathematical Physics

JOURNAL=Frontiers in Physics

VOLUME=8

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00309

DOI=10.3389/fphy.2020.00309

ISSN=2296-424X

ABSTRACT=<p>In this paper we introduce the (<italic>k, s</italic>)-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 (<italic>k, s</italic>)-Hilfer-Prabhakar derivative.</p>