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Applications of Subordination Chains and Fractional Integral in Fuzzy Differential Subordinations

Author

Listed:
  • Georgia Irina Oros

    (Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, Romania)

  • Simona Dzitac

    (Department of Energy Engineering, Faculty of Energy Engineering and Industrial Management, University of Oradea, Universitatii 1, 410087 Oradea, Romania)

Abstract

Fuzzy differential subordination theory represents a generalization of the classical concept of differential subordination which emerged in the recent years as a result of embedding the concept of fuzzy set into geometric function theory. The fractional integral of Gaussian hypergeometric function is defined in this paper and using properties of the subordination chains, new fuzzy differential subordinations are obtained. Dominants of the fuzzy differential subordinations are given and using particular functions as such dominants, interesting geometric properties interpreted as inclusion relations of certain subsets of the complex plane are presented in the corollaries of the original theorems stated. An example is constructed as an application of the newly proved results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1690-:d:815981
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    References listed on IDEAS

    as
    1. José A. Antonino & Sanford S. Miller, 2021. "Systems of Simultaneous Differential Inclusions Implying Function Containment," Mathematics, MDPI, vol. 9(11), pages 1-10, May.
    2. 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.
    3. Alina Alb Lupaş, 2021. "Applications of the Fractional Calculus in Fuzzy Differential Subordinations and Superordinations," Mathematics, MDPI, vol. 9(20), pages 1-10, October.
    4. Lupaş, Alina Alb & Oros, Gheorghe, 2015. "On special fuzzy differential subordinations using Sălăgean and Ruscheweyh operators," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 119-127.
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    Citations

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    Cited by:

    1. 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.
    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.

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