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On ν -Level Interval of Fuzzy Set for Fractional Order Neutral Impulsive Stochastic Differential System

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  • Manjitha Mani Shalini

    (Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore 641202, Tamil Nadu, India
    Department of Mathematics and Computer Applications, PSG College of Arts and Science, Coimbatore 641014, Tamil Nadu, India)

  • Nazek Alessa

    (Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Banupriya Kandasamy

    (Department of Mathematics and Computer Applications, PSG College of Arts and Science, Coimbatore 641014, Tamil Nadu, India)

  • Karuppusamy Loganathan

    (Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur 303007, Rajasthan, India)

  • Maheswari Rangasamy

    (Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore 641202, Tamil Nadu, India)

Abstract

The main concern of this paper is to investigate the existence and uniqueness of a fuzzy neutral impulsive stochastic differential system with Caputo fractional order driven by fuzzy Brownian motion using fuzzy numbers with bounded ν -level intervals that are convex, normal and upper-semicontinuous. Fuzzy Itô process, Grönwall’s inequality and the Banach fixed-point theorem are employed to probe the local and global existence. An analytical example is provided to examine the theoretical results.

Suggested Citation

  • Manjitha Mani Shalini & Nazek Alessa & Banupriya Kandasamy & Karuppusamy Loganathan & Maheswari Rangasamy, 2023. "On ν -Level Interval of Fuzzy Set for Fractional Order Neutral Impulsive Stochastic Differential System," Mathematics, MDPI, vol. 11(9), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:1990-:d:1130720
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    References listed on IDEAS

    as
    1. Marek T. Malinowski, 2016. "Bipartite Fuzzy Stochastic Differential Equations with Global Lipschitz Condition," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-13, December.
    2. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    3. Valliammal, N. & Ravichandran, C. & Nisar, Kottakkaran Sooppy, 2020. "Solutions to fractional neutral delay differential nonlocal systems," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
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