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Generalized Hukuhara Weak Solutions for a Class of Coupled Systems of Fuzzy Fractional Order Partial Differential Equations without Lipschitz Conditions

Author

Listed:
  • Fan Zhang

    (College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China)

  • Heng-You Lan

    (College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China
    South Sichuan Center for Applied Mathematics, Zigong 643000, China)

  • Hai-Yang Xu

    (College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China)

Abstract

As is known to all, Lipschitz condition, which is very important to guarantee existence and uniqueness of solution for differential equations, is not frequently satisfied in real-world problems. In this paper, without the Lipschitz condition, we intend to explore a kind of novel coupled systems of fuzzy Caputo Generalized Hukuhara type (in short, gH -type) fractional partial differential equations. First and foremost, based on a series of notions of relative compactness in fuzzy number spaces, and using Schauder fixed point theorem in Banach semilinear spaces, it is naturally to prove existence of two classes of gH -weak solutions for the coupled systems of fuzzy fractional partial differential equations. We then give an example to illustrate our main conclusions vividly and intuitively. As applications, combining with the relevant definitions of fuzzy projection operators, and under some suitable conditions, existence results of two categories of gH -weak solutions for a class of fire-new fuzzy fractional partial differential coupled projection neural network systems are also proposed, which are different from those already published work. Finally, we present some work for future research.

Suggested Citation

  • Fan Zhang & Heng-You Lan & Hai-Yang Xu, 2022. "Generalized Hukuhara Weak Solutions for a Class of Coupled Systems of Fuzzy Fractional Order Partial Differential Equations without Lipschitz Conditions," Mathematics, MDPI, vol. 10(21), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4033-:d:958388
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    References listed on IDEAS

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    1. Humaira & Muhammad Sarwar & Thabet Abdeljawad & Nabil Mlaiki, 2021. "Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations," Mathematics, MDPI, vol. 9(16), pages 1-17, August.
    2. Yang, He & Zhao, Yanxia, 2021. "Existence and optimal controls of non-autonomous impulsive integro-differential evolution equation with nonlocal conditions," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
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    Cited by:

    1. Qayyum, Mubashir & Tahir, Aneeza & Saeed, Syed Tauseef & Akgül, Ali, 2023. "Series-form solutions of generalized fractional-fisher models with uncertainties using hybrid approach in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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