Generalized Extended Confluent, Whittaker $k$-functions and Their Properties (European Journal of Pure and Applied Mathematics, 2025)
The main objective of this research paper is to explore further generalization of confluent hypergeometric and Whittaker functions by introducing a new parameter $k>0$, in generalized extended confluent hypergeometric and Whittaker functions defined by Khan et al. \cite{m7}. We also investigate some properties such as integral representations, Mallin transforms, Hankel, Laplace transformations and derivative of these new generalized extended confluent hypergeometric and Whittaker $k$-functions. We also obtain Riemann-Liouville fractional integral and Riemann-Liouville $k$-fractional integral of these new generalized extended Whittaker $k$-function.