A family of meromorphic functions involving generalized Mittag-Leffler function

Abstract

We introduce a new family of meromorphic functions defined by the second order differential subordination involving generalized Mittag-Leffler function. Certain convolution properties of the family are discussed.Mathematics subject classification (2010): 33E12, 30C45.

Subclasses of analytic and bi-univalent functions involving a generalized Mittag-Leffler function based on quasi-subordination

“…Another important and interesting fact about Mittag-Leffler function is that the one and two-parametric Mittag-Leffler functions are fractional extensions of the basic functions. Observe that the function E α,β takes many well-known functions as its special case, for example, [20,28,30,70] and references therein. We note that Mittag-Leffler function E α,β (z) does not belong to the family A.…”

Certain Properties on Meromorphic Functions Defined by a New Linear Operator Involving the Mittag-Leffler Function

“…Some other authors have studied various classes of meromorphic univalent functions, such as, see [3,6,7,20,28] and [30]). Such works encouraged us to create the new class T τ α,µ (a m , b r , d) of Σ, that includes the operator J α,µ h (z), and it is presented as follows.…”