Generalized Extended Confluent, Whittaker k-Functions and Their Properties

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. [1]. We also investigate the Mellin transformations, inverse Mellin transformations, Hankel transformations, Laplace transformations, and derivative of the newly defined generalized extended confluent hy-pergeometric 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.