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An Application to Nonlinear Fractional Differential Equation via α -Γ F -Fuzzy Contractive Mappings in a Fuzzy Metric Space

Author

Listed:
  • Uma Devi Patel

    (Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur 495009, India)

  • Stojan Radenović

    (Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia)

Abstract

In this paper, we first introduce a new family of functions like an implicit function called Γ -functions. Furthermore, we introduce a new concept of α - Γ F -fuzzy contractive mappings, which is weaker than the class of fuzzy F -contractive mappings. Then, the existence and uniqueness of the fixed point are established for a new type of fuzzy contractive mappings in the setting of fuzzy metric spaces. Moreover, some examples and an application to nonlinear fractional differential equation are given, and these show the importance of the introduced theorems in fuzzy settings.

Suggested Citation

  • Uma Devi Patel & Stojan Radenović, 2022. "An Application to Nonlinear Fractional Differential Equation via α -Γ F -Fuzzy Contractive Mappings in a Fuzzy Metric Space," Mathematics, MDPI, vol. 10(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2831-:d:883936
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    References listed on IDEAS

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    1. Huaping Huang & Vesna Todorčević & Stojan Radenović, 2022. "Remarks on Recent Results for Generalized F -Contractions," Mathematics, MDPI, vol. 10(5), pages 1-8, February.
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    Cited by:

    1. Angamuthu Muraliraj & Ravichandran Thangathamizh & Nikola Popovic & Ana Savic & Stojan Radenovic, 2023. "The First Rational Type Revised Fuzzy-Contractions in Revised Fuzzy Metric Spaces with an Applications," Mathematics, MDPI, vol. 11(10), pages 1-11, May.
    2. Malik, Muhammad Faizan & Chang, Ching-Lung & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Kiani, Adiqa kausar & Shu, Chi-Min & Raja, Muhammad Asif Zahoor, 2023. "Swarming intelligence heuristics for fractional nonlinear autoregressive exogenous noise systems," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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