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Large Contractions on Quasi-Metric Spaces with an Application to Nonlinear Fractional Differential Equations

Author

Listed:
  • Erdal Karapınar

    (Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Andreea Fulga

    (Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov, 500036 Brasov, Romania)

  • Maliha Rashid

    (Department of Mathematics & Statistics, International Islamic University, Islamabad H-10 44000, Pakista)

  • Lariab Shahid

    (Department of Mathematics & Statistics, International Islamic University, Islamabad H-10 44000, Pakista)

  • Hassen Aydi

    (Institut Supérieur d’Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia)

Abstract

In this manuscript, we introduce a new notion: a Berinde type ( α , ψ ) -contraction mapping. Thereafter, we investigate not only the existence, but also the uniqueness of a fixed point of such mappings in the setting of right-complete quasi-metric spaces. The result, presented here, not only generalizes a number of existing results, but also unifies several ones on the topic in the literature. An application of nonlinear fractional differential equations is given.

Suggested Citation

  • Erdal Karapınar & Andreea Fulga & Maliha Rashid & Lariab Shahid & Hassen Aydi, 2019. "Large Contractions on Quasi-Metric Spaces with an Application to Nonlinear Fractional Differential Equations," Mathematics, MDPI, vol. 7(5), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:444-:d:232331
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    References listed on IDEAS

    as
    1. Muhammad Usman Ali & Tayyab Kamran & Erdal Karapınar, 2014. "An Approach to Existence of Fixed Points of Generalized Contractive Multivalued Mappings of Integral Type via Admissible Mapping," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, July.
    2. Erdal Karapınar & Bessem Samet, 2012. "Generalized 𠜶 - ð Contractive Type Mappings and Related Fixed Point Theorems with Applications," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, September.
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    Cited by:

    1. Ali Turab & Norhayati Rosli, 2022. "Study of Fractional Differential Equations Emerging in the Theory of Chemical Graphs: A Robust Approach," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    2. Ahmed Refice & Mohammed Said Souid & Ivanka Stamova, 2021. "On the Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order via Kuratowski MNC Technique," Mathematics, MDPI, vol. 9(10), pages 1-16, May.

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