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The Study of Bicomplex-Valued Controlled Metric Spaces with Applications to Fractional Differential Equations

Author

Listed:
  • Gunaseelan Mani

    (Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamil Nadu, India)

  • Salma Haque

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

  • Arul Joseph Gnanaprakasam

    (Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Tamil Nadu, India)

  • Ozgur Ege

    (Department of Mathematics, Ege University, Bornova, 35100 Izmir, Turkey)

  • Nabil Mlaiki

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

Abstract

In this paper, we introduce the concept of bicomplex-valued controlled metric spaces and prove fixed point theorems. Our results mainly focus on generalizing and expanding some recently established results. Finally, we explain an application of our main result to a certain type of fractional differential equation.

Suggested Citation

  • Gunaseelan Mani & Salma Haque & Arul Joseph Gnanaprakasam & Ozgur Ege & Nabil Mlaiki, 2023. "The Study of Bicomplex-Valued Controlled Metric Spaces with Applications to Fractional Differential Equations," Mathematics, MDPI, vol. 11(12), pages 1-19, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2742-:d:1173067
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    References listed on IDEAS

    as
    1. Nabil Mlaiki & Hassen Aydi & Nizar Souayah & Thabet Abdeljawad, 2018. "Controlled Metric Type Spaces and the Related Contraction Principle," Mathematics, MDPI, vol. 6(10), pages 1-7, October.
    2. Muhammad Suhail Aslam & Monica Felicia Bota & Mohammad S. R. Chowdhury & Liliana Guran & Naeem Saleem, 2021. "Common Fixed Points Technique for Existence of a Solution of Urysohn Type Integral Equations System in Complex Valued b -Metric Spaces," Mathematics, MDPI, vol. 9(4), pages 1-18, February.
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    Cited by:

    1. Badriah Alamri, 2024. "Fixed Point Theory in Bicomplex Metric Spaces: A New Framework with Applications," Mathematics, MDPI, vol. 12(11), pages 1-20, June.

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