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Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator

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  • Faten Fakher Abdulnabi

    (Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq
    Ministry of Education, Al-Rusafa 2, Baghdad 10082, Iraq)

  • Hiba F. Al-Janaby

    (Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq)

  • Firas Ghanim

    (Department of Mathematics, College of Sciences, University of Sharjah, Sharjah 27272, United Arab Emirates)

  • Alina Alb Lupaș

    (Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania)

Abstract

In this study, we explore the implications of a third-order differential subordination in the context of analytic functions associated with fractional differential operators. Our investigation involves the consideration of specific admissible classes of third-order differential functions. We also extend this exploration to establish a dual principle, resulting in a sandwich-type outcome. We introduce these admissible function classes by employing the fractional derivative operator D z α S N , S ϑ z and derive conditions on the normalized analytic function f that lead to sandwich-type subordination in combination with an appropriate fractional differential operator.

Suggested Citation

  • Faten Fakher Abdulnabi & Hiba F. Al-Janaby & Firas Ghanim & Alina Alb Lupaș, 2023. "Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:4021-:d:1245159
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    References listed on IDEAS

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    1. Srivastava, H.M. & Gaboury, S. & Ghanim, F., 2015. "A unified class of analytic functions involving a generalization of the Srivastava–Attiya operator," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 35-45.
    2. Baleanu, Dumitru & Wu, Guo–Cheng & Zeng, Sheng–Da, 2017. "Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 99-105.
    3. Huo Tang & H. M. Srivastava & Shu-Hai Li & Li-Na Ma, 2014. "Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, July.
    4. F. Ghanim & Hiba F. Al-Janaby & Marwan Al-Momani & Belal Batiha, 2022. "Geometric Studies on Mittag-Leffler Type Function Involving a New Integrodifferential Operator," Mathematics, MDPI, vol. 10(18), pages 1-10, September.
    5. Adel A. Attiya & Mohamed K. Aouf & Ekram E. Ali & Mansour F. Yassen, 2021. "Differential Subordination and Superordination Results Associated with Mittag–Leffler Function," Mathematics, MDPI, vol. 9(3), pages 1-11, January.
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    Cited by:

    1. 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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