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...

Full description

Saved in:
Bibliographic Details
Published in:Fractal and fractional 2023-10, Vol.7 (10), p.715
Main Authors: Khan, Nazar, Khan, Kashif, Tawfiq, Ferdous, Ro, Jong-Suk, Al-shbeil, Isra
Format: Article
Language:English
Subjects:
analytic functions
Calculus
conic domains
Convex analysis
Differential calculus
Differential equations
Investigations
Operators (mathematics)
Partial differential equations
q -calculus
q -convex functions
q -difference operator
q -starlike functions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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, Λβ,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.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7100715