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

• Hasanen A. Hammad ^[1] ; Hassen Aydi ^[2] ; Doha A. Kattan ^[3]
  1. [1] Qassim University & Sohag University
  2. [2] Sefako Makgatho Health Sciences University & Université de Sousse, China Medical University &
  3. [3] King Abdulaziz University

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 2, 2024
• Idioma: inglés
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• Resumen

  • 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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