Resumen de New Contributions to Fixed Point Techniques with Applications for Solving Fractional and Differential Equations
Hasanen A. Hammad, Hassen Aydi, Doha A. Kattan
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.
