On a fractional class of analytic function defined by using a new operator

TL;DR

This paper introduces a new class of fractional analytic functions in the unit disk, defining a generalized operator that extends classical differential operators and exploring various geometric and coefficient properties of this class.

Contribution

It proposes a novel fractional class of analytic functions and a new generalized operator combining Salagean and Ruscheweyh derivatives, with comprehensive property analysis.

Findings

Coefficient bounds established

Distortion theorems derived

Radii of starlikeness and convexity determined

Abstract

In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by means of this operator, we introduce an interesting subclass of functions which are analytic and univalent. Furthermore, this effort covers coefficient bounds, distortions theorem, radii of starlikeness, convexity, bounded turning, extreme points and integral means inequalities of functions belongs to this class. Finally, applications involving certain fractional operators are illustrated.