FRACTIONAL INTEGRAL OF WHITTAKER k-FUNCTION AND ITS PROPERTIES.

In this paper, we introduce a generalized form of Whittaker function with the help of generalized conuent k-hypergeometric function. We establish several interesting properties of the Whittaker k-function such as its integral representations, derivative, Laplace transform and Hankel transform. Further, we investigate the Riemann-Liouville fractional integral and k-Riemann-Liouville fractional integral of Whittaker k-function. Some intriguing particular cases of the main results are also mentioned. [ABSTRACT FROM AUTHOR]