In this study, the generalized $(p,q)$-derivative operator is used to define a novel class of bi-univalent functions. For this class, we define constraints on the coefficients up to $|{\ell }_5|$. The functions are analyzed using a suitable operational method, which enables us to derive new bounds for the Fekete–Szegö functional, as well as explicit estimates for important coefficients like $|{\ell }_2|$ and $|{\ell }_3|$. In addition, we establish the upper bounds of the second and third Hankel determinants, providing insights into the geometrical and analytical properties of this class of functions.

In this paper, we introduce a novel operator formed by the convolution of the Jung-Kim-Srivastav operator and the Wright function. This operator is used to construct classes of analytic functions within the open unit disk. The primary objective is to establish precise estimates for the basic coefficients |a2| and |a3| in the Taylor-Maclaurin series for functions belonging to this class. Furthermore, we present new results related to this study.

In this paper, a novel class of meromorphic functions associated with the Mittag–Leffler function $E_{\mu ,\vartheta }\left(z\right)$ is introduced using the Hilbert space operator. In the punctured symmetric domain ${⋓}^{\ast }$, essential properties of this class are systematically investigated. These properties include coefficient inequalities, growth and distortion bounds, as well as weighted and arithmetic mean estimates. Furthermore, the extreme points and radii of geometric properties such as close-to-convexity, starlikeness, and convexity are analyzed in detail. Additionally, the Hadamard product (or convolution) is explored to demonstrate the algebraic structure and stability of the introduced function class under this operation. Integral mean inequalities are also established to provide further insights into the behavior of these functions within the given domain.

In this work, we introduce the SEE (Sadiq, Emad, Eman) integral transform to find the general solution of the first order complex differential equations with constant coefficients. The usage of SEE integral transform has proven its efficiency in solving a wide range of linear operator equations.

In this paper we have studied a generalization of a class of ( w-valent ) functions with two fixed points involving hypergeometric function with generalization integral operator . We obtain some results like, coefficient estimates and some theorems of this class.