Certain New Class of Analytic Functions Defined by Using a Fractional Derivative and Mittag-Leffler Functions

Abstract

Fractional calculus has a number of applications in the field of science, specially in mathematics. In this paper, we discuss some applications of fractional differential operators in the field of geometric function theory. Here, we combine the fractional differential operator and the Mittag-Leffler functions to formulate and arrange a new operator of fractional calculus. We define a new class of normalized analytic functions by means of a newly defined fractional operator and discuss some of its interesting geometric properties in open unit disk.