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Applications of the Fractional Calculus in Fuzzy Differential Subordinations and Superordinations

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  • Alina Alb Lupaş

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

Abstract

The fractional integral of confluent hypergeometric function is used in this paper for obtaining new applications using concepts from the theory of fuzzy differential subordination and superordination. The aim of the paper is to present new fuzzy differential subordinations and superordinations for which the fuzzy best dominant and fuzzy best subordinant are given, respectively. The original theorems proved in the paper generate interesting corollaries for particular choices of functions acting as fuzzy best dominant and fuzzy best subordinant. Another contribution contained in this paper is the nice sandwich-type theorem combining the results given in two theorems proved here using the two theories of fuzzy differential subordination and fuzzy differential superordination.

Suggested Citation

  • Alina Alb Lupaş, 2021. "Applications of the Fractional Calculus in Fuzzy Differential Subordinations and Superordinations," Mathematics, MDPI, vol. 9(20), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2601-:d:657664
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    References listed on IDEAS

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    1. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
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    Cited by:

    1. 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.
    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. Sorin Nădăban, 2022. "Fuzzy Logic and Soft Computing—Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921–2017)," Mathematics, MDPI, vol. 10(17), pages 1-3, September.

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