On a unification of Mittag-Leffler function and Wright function - CHUDASAMA, Meera H. (Studia Universitatis Babeș-Bolyai Mathematica, 2025)
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. Mathematics Subject Classification (2010): 26A33, 33E12, 40A05. Received 26 July 2024; Accepted 22 October 2024.