On the (k,s)-Hilfer-Prabhakar Fractional Derivative With Applications to Mathematical Physics
Muhammad Samraiz, Zahida Perveen, Gauhar Rahman, Kottakkaran Sooppy Nisar, Devendra Kumar
Abstract
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.
Topics & Concepts
Laplace transformApplied mathematicsOperator (biology)Fractional calculusMathematicsPhysicsMathematical analysisChemistryTranscription factorRepressorBiochemistryGeneFractional Differential Equations SolutionsMathematical functions and polynomialsIterative Methods for Nonlinear Equations