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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 13, Issue 1


Volume 13 (2015)

Third-order differential subordination and superordination involving a fractional operator

Rabha W. Ibrahim
  • Faculty of Computer Science and Information Technology, University Malaya, 50603 Kuala Lumpur, Malaysia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Muhammad Zaini Ahmad
  • Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Malaysia, E-mail: mzaini@unimap.edu.my
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Hiba F. Al-Janaby
  • Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Malaysia, E-mail: mzaini@unimap.edu.my
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-10-23 | DOI: https://doi.org/10.1515/math-2015-0068


The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.

Keywords: Fractional calculus; Fractional integral operator; Subordination; Superordination; Unit disk; Analytic function


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About the article

Received: 2015-05-08

Accepted: 2015-09-09

Published Online: 2015-10-23

Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0068.

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©2015 Rabha W. Ibrahim et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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