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Fuzzy Approximate Solutions of Matrix-Valued Fractional Differential Equations by Fuzzy Control Functions

Author

Listed:
  • Safoura Rezaei Aderyani

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 1684613114, Iran)

  • Reza Saadati

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 1684613114, Iran)

  • Donal O’Regan

    (School of Mathematical and Statistical Sciences, University of Galway, University Road, H91 TK33 Galway, Ireland)

  • Fehaid Salem Alshammari

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11432, Saudi Arabia)

Abstract

We apply Mittag–Leffler-type functions to introduce a class of matrix-valued fuzzy controllers which help us to propose the notion of multi-stability (MS) and to obtain fuzzy approximate solutions of matrix-valued fractional differential equations in fuzzy spaces. The concept of multi stability allows us to obtain different approximations depending on the different special functions that are initially chosen. Additionally, using various properties of a function of Mittag–Leffler type, we study the Ulam–Hyers stability (UHS) of the models.

Suggested Citation

  • Safoura Rezaei Aderyani & Reza Saadati & Donal O’Regan & Fehaid Salem Alshammari, 2023. "Fuzzy Approximate Solutions of Matrix-Valued Fractional Differential Equations by Fuzzy Control Functions," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1386-:d:1095883
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    References listed on IDEAS

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    1. Baleanu, Dumitru & Shekari, Parisa & Torkzadeh, Leila & Ranjbar, Hassan & Jajarmi, Amin & Nouri, Kazem, 2023. "Stability analysis and system properties of Nipah virus transmission: A fractional calculus case study," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
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    Cited by:

    1. Safoura Rezaei Aderyani & Reza Saadati & Donal O’Regan & Fehaid Salem Alshammari, 2024. "Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects," Mathematics, MDPI, vol. 12(6), pages 1-31, March.

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