On a unification of Mittag-Leffler function and Wright function

We introduce here a function that unifies Mittag-Leffler function and Wright function which is referred to here as an UMLW-function. This function turns out to be a solution of an infinite order differential equation. With the aid of this UMLW-function, an integral operator is constructed and shown that it is bounded in Lebesgue measurable space. Further an eigen function property is established for a particular UMLW-function with the help of hyper-Bessel operator and Caputo fractional derivative operator. Some well known functions occur in the illustrations of these properties. At the end, the graphs of this UMLW-function are plotted by suitably specializing the parameters and also compared with the graph of exponential as well as Mittag-Leffler function.