On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative

Abstract

Fractional calculus is the prominent branch of applied mathematics, it deals with a lot of diverse possibility of finding differentiation as well as integration of function <i>f</i>(<i>z</i>) when the order of differentiation operator ‘D’ and integration operator ‘J’ is a real number or a complex number. The combination of fractional calculus with geometric function theory is the dynamic field of the current research scenario. It has many applications not only in the field of mathematics but also in the different fields like modern mathematical physics, electrochemistry, viscoelasticity, fluid dynamics, electromagnetic, the theory of partial differential equations systems, Mathematical modeling. Various new subclasses of univalent and multivalent functions defined by using different operators. In this research paper, we work on the formation of new subclass of analytic and multivalent functions defined under the open unit disk. By using Generalized Ruscheweyh derivative operator we define a new subclass of analytic and multivalent functions. The main aim of this research article is to derive interesting characteristics of new subclass of multivalent functions, which mainly include coefficient bound, growth and distortion bounds for function and its first derivative, extreme point and obtain unidirectional results for the multivalent functions which are belonging to this new subclass.