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 languageEnglish
Article number325
JournalAdvances in Difference Equations
Volume2020
DOIs
Publication statusPublished - 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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