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The aim of this study is to investigate a certain sufficiency criterion for uniform convexity, strong starlikeness, and strong convexity of Rabtonov fractional exponential functions. We also study the starlikeness and convexity of order  γ. Moreover, we find conditions so that the Rabotnov functions belong to the class of bounded analytic functions and Hardy spaces. Various consequences of these results are also presented. [ABSTRACT FROM AUTHOR]

In this study, we begin by examining the τ -fractional differintegral operator and proceed to establish a novel subclass in the open unit disk E. The determination of the nth coefficient bound for functions within this recently established class is accomplished by the use of the Faber polynomial expansion approach. Additionally, we examine the behavior of the initial coefficients of bi-close-to-convex functions defined by the τ -fractional differintegral operator, which may exhibit unexpected reactions. We established connections between our current research and prior studies in order to validate our significant findings. [ABSTRACT FROM AUTHOR]

This article extends the study of q-versions of analytic functions by introducing and studying the association of starlike functions with trigonometric cosine functions, both defined in their q-versions. Certain coefficient inequalities like coefficient bounds, Zalcman inequalities, and both Hankel and Toeplitz determinants for the new version of starlike functions are investigated. It is worth mentioning that most of the determined inequalities are sharp with the support of relevant extremal functions. [ABSTRACT FROM AUTHOR]

In this paper, we use the concept of quantum (or q -) calculus and define a q -analogous of a fractional differential operator and discuss some of its applications. We consider this operator to define new subclasses of uniformly q -starlike and q -convex functions associated with a new generalized conic domain, Λ β , q , γ . To begin establishing our key conclusions, we explore several novel lemmas. Furthermore, we employ these lemmas to explore some important features of these two classes, for example, inclusion relations, coefficient bounds, Fekete–Szego problem, and subordination results. We also highlight many known and brand-new specific corollaries of our findings. [ABSTRACT FROM AUTHOR]

This article investigates inequalities for certain types of strongly convex functions by applying q-h-integrals. These inequalities provide the refinements of some well-known results that hold for (α , m) - and (ℏ - m) -convex and related functions. Inequalities for q-integrals are deducible by vanishing the parameter h. Some particular cases are discussed after proving the main results. [ABSTRACT FROM AUTHOR]

This paper aims to study the bounds of k-integral operators with the Mittag-Leffler kernel in a unified form. To achieve these bounds, the definition of exponentially (α , h − m) − p -convexity is utilized frequently. In addition, a fractional Hadamard type inequality which shows the upper and lower bounds of k-integral operators simultaneously is presented. The results are directly linked with the results of many published articles. [ABSTRACT FROM AUTHOR]