On subclasses of analytic functions based on a quantum symmetric conformable differential operator with application

Rabha W. Ibrahim; Rafida M. Elobaid; Suzan J. Obaiys

doi:10.1186/s13662-020-02788-6

On subclasses of analytic functions based on a quantum symmetric conformable differential operator with application

Rabha W. Ibrahim, Rafida M. Elobaid, Suzan J. Obaiys

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Abstract

Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators, integral operators, and classes of analytic functions, especially the classes that are generated by convolution product (Hadamard product). In this effort, we aim to introduce a quantum symmetric conformable differential operator (Q-SCDO). This operator generalized some well-know differential operators such as Sàlàgean differential operator. By employing the Q-SCDO, we present subclasses of analytic functions to study some of its geometric solutions of q-Painlevé differential equation (type III).

Original language	English
Article number	325
Journal	Advances in Difference Equations
Volume	2020
DOIs	https://doi.org/10.1186/s13662-020-02788-6
Publication status	Published - 1 Jul 2020

Keywords

Analytic function
Conformable fractional derivative
Open unit disk
Subordination and superordination
Univalent function

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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