Geometric Properties of a Linear Complex Operator on a Subclass of Meromorphic Functions: An Analysis of Hurwitz-Lerch-Zeta Functions

Abstract

Geometric function theory (GFT) is one of the richest research disciplines in complex analysis. This discipline also deals with the extended differential inequality theory, known as the differential subordination theory. Based on these theories, this study focuses on analyzing intriguing aspects of the geometric subclass of meromorphic functions in terms of a linear complex operator and a special class of Hurwitz-Lerch-Zeta functions. Hence, several of its geometric attributes are deduced. Furthermore, the paper highlights the different fascinating advantages and applications of various new geometric subclasses in relation to the subordination and inclusion theorems.

Geometric Features of the Hurwitz–Lerch Zeta Type Function Based on Differential Subordination Method

“…Garg et al [26], Jankov et al [27], Srivastava et al [28], Choi and R.K. Parmar [29], Ghanim et al [30], Ghanim and Al-Janaby [31], Al-Janaby and Ghanim [32], Nisar [33], Nadeem et al [34], Reynolds and Stauffer [35], and Mehrez and Agarwal [36].…”

On the Dynamics of the Complex Hirota-Dynamical Model

“…Mathematical models provide the most effective explanations for natural physical phenomena, and these models often involve the formulation of both linear and nonlinear differential equations to represent dynamical systems [1,2]. The examination of results derived from nonlinear partial differential equations (NPDEs) has become a crucial component across various fields of science and technology, including physical sciences, fluid mechanics, fiber optics, solid-state mechanics, and material sciences [3,4].…”