The k-fractional Hilfer derivative

Abstract

In this paper we study a k-version of the fractional derivative of two parameter introduced by Hilfer in [4], we calculate its Laplace transform and calculate the derivative of some functions. Also study a new operator that contains in its kernel the k-Mittag-Leffler function introduced by authors in [3]. Finally, we generalize and solve a fractional differential equation propuse by Srivastava-Tomovsky in [9].