In this paper, we study the extended Mittag -Leffler function by using generalized beta function and obtain various differential properties, integral representations. Further, we discuss Mellin transform of these functions in terms of generalized Wright hyper geometric function and evaluate Laplace transform, and Whittaker transform in terms of extended beta function. Finally, several interesting special cases of extended Mittag -Leffler functions have also be given.
Mittal, Ekta; Pandey, Rupakshi M.; and Joshi, Sunil
ON EXTENSION OF MITTAG-LEFFLER FUNCTION,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 11,
1, Article 20.
Available at: https://digitalcommons.pvamu.edu/aam/vol11/iss1/20