Generalized extended Mittag-Leffler function and its properties pertaining to integral transforms and fractional calculus

Abstract

We aim to introduce extended generalized Mittag-Leffler function (EGMLF) via the extended Beta function and obtain certain integral and differential representation of them. Further, we present some formulas of the Riemann-–Liouville fractional integration and differentiation operators. Also, we derive various integral transforms, including Euler transform, Laplace transform, Whittakar transform and K-transform. The operator and transform images are expressed in terms of the Wright generalized hypergoemetrichypergeometric type function. Interesting special cases of the main results are also considered.