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Fuzzy Mittag–Leffler–Hyers–Ulam–Rassias Stability of Stochastic Differential Equations

Author

Listed:
  • Reza Chaharpashlou

    (Department of Mathematics, Jundi-Shapur University of Technology, Dezful 64615-334, Iran)

  • Reza Saadati

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran)

  • António M. Lopes

    (LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal)

Abstract

Stability is the most relevant property of dynamical systems. The stability of stochastic differential equations is a challenging and still open problem. In this article, using a fuzzy Mittag–Leffler function, we introduce a new fuzzy controller function to stabilize the stochastic differential equation (SDE) ν ′ ( γ , μ ) = F γ , μ , ν ( γ , μ ) . By adopting the fixed point technique, we are able to prove the fuzzy Mittag–Leffler–Hyers–Ulam–Rassias stability of the SDE.

Suggested Citation

  • Reza Chaharpashlou & Reza Saadati & António M. Lopes, 2023. "Fuzzy Mittag–Leffler–Hyers–Ulam–Rassias Stability of Stochastic Differential Equations," Mathematics, MDPI, vol. 11(9), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2154-:d:1139124
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    References listed on IDEAS

    as
    1. M. M. Pourpasha & Th. M. Rassias & R. Saadati & S. M. Vaezpour, 2011. "The Stability of Some Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-15, December.
    2. Salvador Romaguera & Pedro Tirado, 2020. "Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results," Mathematics, MDPI, vol. 8(2), pages 1-7, February.
    3. Arshad Ali & Vidushi Gupta & Thabet Abdeljawad & Kamal Shah & Fahd Jarad, 2020. "Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-16, November.
    4. A. Naimi & B. Tellab & Y. Altayeb & A. Moumen, 2021. "Generalized Ulam–Hyers–Rassias Stability Results of Solution for Nonlinear Fractional Differential Problem with Boundary Conditions," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-11, November.
    5. P. Agilan & Mohammed M. A. Almazah & K. Julietraja & Ammar Alsinai, 2023. "Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces," Mathematics, MDPI, vol. 11(3), pages 1-19, January.
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