On Application of Fractional Differintegral Operator to the K4- Function

The object of this paper is to introduce a new function called K_4-function defined by the author in terms of some special functions, which is an extension of the G-function defined by Lorenzo and Hartley [4] and demonstrate how K_4-function is closely related to another special functions, namely Lorenzo-Hartleya’s R-function, Robotnov and Hartleya’s F-function, Mittag-Leffler function, generalized Mittag-Leffler function, Exponential function. The differintegration of that function is also investigated. As special cases most of the results obtained in this paper are believed to be new and include some of the results given earlier by other authors.