  In this paper we define the regularized version of k-Prabhakar fractional
derivative, k-Hilfer-Prabhakar fractional derivative, regularized version of
k-Hilfer-Prabhakar fractional derivative and find their Laplace and Sumudu
transforms. Using these results, the relation between k-Prabhakar fractional
derivative and its regularized ver- sion involving k-Mittag-Leffler function is
obtained. Similarly the relation between k-Hilfer-Prabhakar fractional
derivative and its regularized version is also obtained. Further, we find the
solutions of some problems in physics in which k-Hilfer-Prabhakar fractional
derivative and its regularized version are involved.
