Some properties of a linear operator involving generalized Mittag-Leffler function

Abstract

This paper introduces a new class T γ α,β,k (η) of analytic functions which is defined by means of a linear operator involving generalized Mittag-Leffler function H γ α,β,k (f ). The results investigated in this paper include, an inclusion relation for functions in the class T γ α,β,k (η) and also some subordination results of the linear operator H γ α,β,k (f ). Several consequences of our results are also pointed out. Mathematics Subject Classification (2010): 33E12, 30C45.

Fuzzy Differential Subordinations Based upon the Mittag-Leffler Type Borel Distribution

“…Some important examples include fractionalorder generalizations of the kinetic equation, random walks, Lévy flights, super-diffusive transport and the study of complex systems. Potentially useful properties of the Mittag-Leffler-type functions E α (z) and E α,β (z) can be found in, for example, [28,[32][33][34][35][36][37][38].…”

Bi-Bazilevič functions based on the Mittag-Leffler-type Borel distribution associated with Legendre polynomials

“…The Mittag-Leffler function arises naturally in the solution of fractional order differential and integral equations, and especially in the investigations of fractional generalization of kinetic equation, random walks, Lévy flights, superdiffusive transport and in the study of complex systems. Several properties of Mittag-Leffler function and generalized Mittag-Leffler function can be found, e.g., in [4,5,14,15,17,22,33]. Observe that Mittag-Leffler function E α,β (z) does not belong to the family A.…”

An application of Mittag–Leffler-type Poisson distribution on certain subclasses of analytic functions associated with conic domains

“…Several properties of Mittag-Leffler function and generalized Mittag-Leffler function can be found e.g. in [23,24,25,26,27,28]. Observe that Mittag-Leffler function , does not belong to the family .…”