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New Contributions to Fixed Point Techniques with Applications for Solving Fractional and Differential Equations

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Abstract

In this article, we present two novel ideas of f-contractions, named dual \(f^{*}\)-weak rational contractions and triple \(f^{*}\)-weak rational contractions, generalizing and expanding many of the solid results in this direction. The endeavor to apply the generalized Banach contraction principle to the set of f-contraction type mappings by applying numerous f-type functions gave rise to these novel generalizations. Also, under appropriate conditions, related unique fixed-point theorems are established. Moreover, some illustrative examples are given to support and strengthen the theoretical results. Furthermore, the obtained results are applied to discuss the existence of solutions to a fractional integral equation and a second-order differential equation. Finally, the significance of the new results and some future work are presented.

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Authors and Affiliations

  1. Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, 52571, Buraydah, Saudi Arabia

    Hasanen A. Hammad

  2. Department of Mathematics, Faculty of Science, Sohag University, Sohâg, 82524, Egypt

    Hasanen A. Hammad

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

    Hassen Aydi

  4. China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Hassen Aydi

  5. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

    Hassen Aydi

  6. Department of Mathematics, College of Sciences and Art, King Abdulaziz University, Rabigh, Saudi Arabia

    Doha A. Kattan

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  1. Hasanen A. Hammad
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  2. Hassen Aydi
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  3. Doha A. Kattan
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All authors contributed equally and significantly in writing this article.

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Correspondence to Hassen Aydi.

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Hammad, H.A., Aydi, H. & Kattan, D.A. New Contributions to Fixed Point Techniques with Applications for Solving Fractional and Differential Equations. Qual. Theory Dyn. Syst. 23, 71 (2024). https://doi.org/10.1007/s12346-023-00932-7

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  • DOI: https://doi.org/10.1007/s12346-023-00932-7

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