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

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, Lambda(beta,q,gamma). 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.

Automated summary

In this paper, the concept of quantum calculus is used to define a q-analogous of a fractional differential operator and explore its applications. New subclasses of uniformly q-starlike and q-convex functions are defined using this operator in association with a new generalized conic domain, Lambda(beta,q,gamma). The paper presents novel lemmas and investigates important features of these function classes, including inclusion relations, coefficient bounds, Fekete-Szego problem, and subordination results. The findings also lead to several known and new specific corollaries.