Applications of Fractional Differential Operator to Subclasses of Uniformly q-Starlike Functions

초록

In this paper, we use the concept of quantum (or (Formula presented.) -) calculus and define a (Formula presented.) -analogous of a fractional differential operator and discuss some of its applications. We consider this operator to define new subclasses of uniformly (Formula presented.) -starlike and (Formula presented.) -convex functions associated with a new generalized conic domain, (Formula presented.). 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. © 2023 by the authors.

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