A Specific Class of Harmonic Meromorphic Functions Associated with the Mittag-Leffler Transformation

Abstract

This article uses the Mittag-Leffler transformation to explore a specific category of harmonic meromorphic functions. The Mittag-Leffler transformation is a crucial tool for analysing meromorphic functions and provides essential properties and insights into their behavior. The main focus of this study is on harmonic meromorphic functions that can be represented by the Mittag-Leffler transformation. Furthermore, this research introduces an innovative derivative operator that incorporates this transformation into the domain of harmonic meromorphic functions. The Mittag-Leffler transformation is widely recognised as a powerful technique for analysing various mathematical functions, especially those with fractional order derivatives. It improves our understanding of harmonic meromorphic functions and their inherent characteristics. The research findings highlight the effectiveness of this new derivative operator in unraveling the complexities of these functions. They provide valuable insights into their behavior and fundamental traits. Additionally, the study offers coefficient inequalities, the distortion theorem, distortion bounds, extreme points, convex combinations, and convolution analyses specifically tailored to functions within this particular class.