This paper introduces a new fractional operator by using the concepts of q-calculus and q-Mittag-Leffler functions. With this operator, Janowski functions are generalized studied regarding their certain geometric characteristics. It also establishes solution complex Briot–Bouquet differential equation newly defined operator.

We define a new subclass of univalent function based on Salagean differential operator and obtained the initial Taylor coefficients using the techniques of Briot-Bouquet differential subordination in association with the modified sigmoid function. Further we obtain the classical Fekete-Szego inequality results.

By applying the principle of differential subordination between analytic functions to a substantially general family of linear transformations, we derive an extension of the Briot-Bouquet differential subordination relations given in the monograph on the subject by Miller and Mocanu [8]. We also present a systematic discussion of various other linear transformations associated with differential...

The object of the present paper is to derive various properties and characteristics of certain subclasses of p-valently analytic functions of order α in the open unit disc by using the techniques involving the Briot-Bouquet differential subordination. MSC 2000. 30C45.