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Fuzzy Differential Subordination and Superordination Results for Fractional Integral Associated with Dziok-Srivastava Operator

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  • Alina Alb Lupaş

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

Abstract

Fuzzy set theory, introduced by Zadeh, gives an adaptable and logical solution to the provocation of introducing, evaluating, and opposing numerous sustainability scenarios. The results described in this article use the fuzzy set concept embedded into the theories of differential subordination and superordination from the geometric function theory. In 2011, fuzzy differential subordination was defined as an extension of the classical notion of differential subordination, and in 2017, the dual concept of fuzzy differential superordination appeared. These dual notions are applied in this paper regarding the fractional integral applied to Dziok–Srivastava operator. New fuzzy differential subordinations are proved using known lemmas, and the fuzzy best dominants are established for the obtained fuzzy differential subordinations. Dual results regarding fuzzy differential superordinations are proved for which the fuzzy best subordinates are shown. These are the first results that link the fractional integral applied to Dziok–Srivastava operator to fuzzy theory.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3129-:d:1194688
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    References listed on IDEAS

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    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. 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. Patchara Phochanikorn & Chunqiao Tan, 2019. "A New Extension to a Multi-Criteria Decision-Making Model for Sustainable Supplier Selection under an Intuitionistic Fuzzy Environment," Sustainability, MDPI, vol. 11(19), pages 1-24, September.
    4. Alina Alb Lupaş, 2021. "Applications of the Fractional Calculus in Fuzzy Differential Subordinations and Superordinations," Mathematics, MDPI, vol. 9(20), pages 1-10, October.
    5. Thi-Ly Nguyen & Phi-Hung Nguyen & Hong-Anh Pham & Thi-Giang Nguyen & Duc-Thinh Nguyen & Thi-Hoai Tran & Hong-Cham Le & Huong-Thuy Phung, 2022. "A Novel Integrating Data Envelopment Analysis and Spherical Fuzzy MCDM Approach for Sustainable Supplier Selection in Steel Industry," Mathematics, MDPI, vol. 10(11), pages 1-28, June.
    6. 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.
    7. 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.
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