On the k-Riemann-Liouville fractional derivative

The main object of this paper is to introduce a new fractional operatorcalled k-Riemann-Liouville fractional derivative defined by usingthe k-Gamma function, which is a generalization of the classicalGamma function. We also investigate relationships with the k-Riemann-Liouville integral and derive some properties by using Fourier and Laplacetransform.