Zainab E. Abdulnaby

Some properties for integro-differential operator defined by a fractional formal

Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator

Jack's lemma for certain subclasses of analytic functions defined by a new fractional linear operator

\mathfrak {J}_{m}(z)

Integral transforms defined by a new fractional class of analytic function in a complex Banach space

Jm(z) defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.

Generalized convolution properties based on the modified Mittag-Leffler function

In this work, we introduce some properties of a complex fractional differential operator. The boundedness and some other properties are studied in view of geometric function theory.

Upper bound of fractional differential operator related to univalent functions

The theory of functional operator has been employed in several areas of mathematics, especially in the geometric function theory in the open unit disk. By utilizing the Moment-Generating function, we define a new fractional linear operator in the open unit disk. We discuss some geometric properties of this operator on some subclasses by applying the concept Jack’s lemma.