On a unification of Mittag-Leffler function and Wright function
DOI:
https://doi.org/10.24193/subbmath.2025.2.02Keywords:
Mittag-Leffler function, Wright function, $\theta$-form differential equation, Fractional derivatives and integralsAbstract
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.
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