Geometric Properties of Harmonic Function Affiliated With Fractional Operator

Abstract

This paper's goal is to discover new results for the harmonic univalent functions G=υ+η defined in the open unit disc ρ={z: |z|<1}. Examining KS indicates the set of all analytic harmonic functions of form G in the open unit disc ρ. The convolution featuring the Mittag-Leffler function and fractional operator is applied to generate the family of harmonic univalent VKS. Motivated by Kamali [9], we present a novel of kamali class with VKS(δ) brand-new class of harmonic univalent functions Pα,β,zγ,δ,ε,ν inspiring inequality. Analysing Mittag-Leffler function convolution with modified tremblay operator inequality as a necessary and sufficient condition for univalent harmonic functions related to specific generalised Mittag-Leffler functions to be in the function class VKS(δ) is the aim of this research. Moreover, we discover extreme points, a distortion theorem, convolution properties, and convex combinations for the functions in VKS(δ).