Applications of nonhomogenous Cauchy-Euler fractional $q$-differential equation to a new class of analytic functions

Document Type : Original Article

Author

Serap Bulut

Kocaeli University, Faculty of Aviation and Space Sciences, Arslanbey Campus, 41285 Kartepe-Kocaeli, Turkey

10.22034/kjm.2023.390830.2818

Abstract

In this paper, we define a new general fractional $q$-differential operator and by means of this operator we introduce a new subclass of analytic functions which are the solutions of the nonhomogenous Cauchy-Euler fractional $q$-differential equations. Our aim is to determine upper bounds of Taylor-Maclaurin coefficients for functions belong to this class.

Keywords

Analytic function

$q$-starlike function

$q$-convex function

fractional $q$-derivative

Cauchy-Euler differential equation

Subjects

• 30 Functions of a complex variable

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