The q-derivative and Hohlov operators have seen much use in recent years. First, numerous well-known principles of the q-derivative operator are highlighted and explained in this research. We then build a novel subclass of analytic and bi-univalent functions using the Hohlov operator and certain q-Chebyshev polynomials. A number of coefficient bounds, as well as the Fekete–Szegö inequalities and the second Hankel determinant are provided for these newly specified function classes.

In the present paper we introduce a new class of analytic functions f in the open unit disk normalized by f (0) = f ^′ (0) − 1 = 0, associated with exponential functions. The aim of the present paper is to investigate the third-order Hankel determinant H ₃ (1) for this function class and obtain the upper bound of the determinant H ₃ (1).

In the present paper, due to beta negative binomial distribution series and Laguerre polynomials, we investigate a new family ${\mathcal{F}}_{\mathsf{\Sigma }}(\delta ,\eta ,\lambda ,\theta ;h)$ of normalized holomorphic and bi-univalent functions associated with Ozaki close-to-convex functions. We provide estimates on the initial Taylor–Maclaurin coefficients and discuss Fekete–Szegő type inequality for functions in this family.

The present paper continues the study on the relatively new concept of fuzzy differential subordination conducted in some recently published cited papers. In this article, certain fuzzy subordination results for analytical functions involving the Atangana–Baleanu fractional integral of Bessel functions are presented. Theorems giving the best dominants for some fuzzy differential subordinations are proved, and interesting corollaries are provided with the use of particular functions as fuzzy best dominants.

In this paper, we introduce two new subclasses of bi-univalent functions using the q-Hermite polynomials. Furthermore, we establish the bounds of the initial coefficients ${\upsilon }_2$, ${\upsilon }_3$, and ${\upsilon }_4$ of the Taylor–Maclaurin series and that of the Fekete–Szegö functional associated with the new classes, and we give the many consequences of our findings.

In this paper, we examine the differential subordination implication related with the Janowski and secant hyperbolic functions. Furthermore, we explore a few results, for example, the necessary and sufficient condition in light of the convolution concept, growth and distortion bounds, radii of starlikeness and partial sums related to the class ${\mathcal{S}}_{sech}^{\ast }.$