Note on a <inline-formula><tex-math id="M1">\begin{document}$ k $\end{document}</tex-math></inline-formula>-generalised fractional derivative

Abstract

In this paper, we introduce the $ k $-generalised fractional derivatives with three parameters which reduced to $ k $-fractional Hilfer derivatives and $ k $-Riemann-Liouville fractional derivative as an interesting special cases. Further, we have also introduced some presumably new fascinating results which include the image power function, Laplace transform and composition of $ k $-Riemann-Liouville fractional integral with generalized composite fractional derivative. The technique developed in this paper can be used in other situation as well.