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

Advances in Difference Equations

article

Ibrahim, Rabha W.¹  Elobaid, Rafida M.³  Obaiys, Suzan J.⁴ 

[1] Informetrics Research Group, Ton Duc Thang University;Faculty of Mathematics & Statistics, Ton Duc Thang University;Department of General Sciences, Prince Sultan University;School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia

关键词: Univalent function;    Conformable fractional derivative;    Subordination and superordination;    Analytic function;    Open unit disk;   

DOI  :  10.1186/s13662-020-02788-6

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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).

【 授权许可】

CC BY