New classes of harmonic functions defined by fractional operator

Abstract

In the present study, we introduce an investigation of new subclasses of harmonic functions which are defined by fractional operator. Firstly, using by fractional operator, we define new subclasses of harmonic functions. Later, we obtain main theorems of our study which contain sufficient and necessary coefficient bounds for functions related to the classes newly defined. Also, several particular characterization properties of these classes are given. Some of these properties involve extreme points, convex combination, distortion bounds. Finally, several corollaries of the main theorems are presented.