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Fuzzy Differential Subordination and Superordination Results Involving the q -Hypergeometric Function and Fractional Calculus Aspects

Author

Listed:
  • Alina Alb Lupaş

    (Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania
    These authors contributed equally to this work.)

  • Georgia Irina Oros

    (Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania
    These authors contributed equally to this work.)

Abstract

The concepts of fuzzy differential subordination and superordination were introduced in the geometric function theory as generalizations of the classical notions of differential subordination and superordination. Fractional calculus is combined in the present paper with quantum calculus aspects for obtaining new fuzzy differential subordinations and superordinations. For the investigated fuzzy differential subordinations and superordinations, fuzzy best subordinates and fuzzy best dominants were obtained, respectively. Furthermore, interesting corollaries emerge when using particular functions, frequently involved in research studies due to their geometric properties, as fuzzy best subordinates and fuzzy best dominants. The study is finalized by stating the sandwich-type results connecting the previously proven results.

Suggested Citation

  • Alina Alb Lupaş & Georgia Irina Oros, 2022. "Fuzzy Differential Subordination and Superordination Results Involving the q -Hypergeometric Function and Fractional Calculus Aspects," Mathematics, MDPI, vol. 10(21), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4121-:d:963699
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    References listed on IDEAS

    as
    1. Simona Dzitac & Sorin Nădăban, 2021. "Soft Computing for Decision-Making in Fuzzy Environments: A Tribute to Professor Ioan Dzitac," Mathematics, MDPI, vol. 9(14), pages 1-11, July.
    2. Georgia Irina Oros & Simona Dzitac, 2022. "Applications of Subordination Chains and Fractional Integral in Fuzzy Differential Subordinations," Mathematics, MDPI, vol. 10(10), pages 1-18, May.
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    Cited by:

    1. Alina Alb Lupaş & Georgia Irina Oros, 2023. "Strong Differential Subordinations and Superordinations for Riemann–Liouville Fractional Integral of Extended q -Hypergeometric Function," Mathematics, MDPI, vol. 11(21), pages 1-15, October.
    2. Alina Alb Lupaş, 2023. "Fuzzy Differential Subordination and Superordination Results for Fractional Integral Associated with Dziok-Srivastava Operator," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
    3. Ekram E. Ali & Georgia Irina Oros & Shujaat Ali Shah & Abeer M. Albalahi, 2023. "Applications of q -Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    4. Abdullah Alsoboh & Ala Amourah & Maslina Darus & Carla Amoi Rudder, 2023. "Studying the Harmonic Functions Associated with Quantum Calculus," Mathematics, MDPI, vol. 11(10), pages 1-11, May.
    5. Georgia Irina Oros & Simona Dzitac & Daniela Andrada Bardac-Vlada, 2024. "Introducing the Third-Order Fuzzy Superordination Concept and Related Results," Mathematics, MDPI, vol. 12(19), pages 1-12, October.

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