Fixed Point Theorems on Controlled Orthogonal δ ‐Metric‐Type Spaces and Applications to Fractional Integrals

In this article, we introduce a notion of controlled orthogonal δ ‐metric‐type spaces with an example. Further, we prove a contraction theorem and a generalized fixed point theorem in controlled orthogonal δ ‐metric‐type spaces. Finally, we illustrate two applications of the obtained fixed point res...

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Bibliographic Details
Published in:Journal of function spaces 2025-01, Vol.2025 (1)
Main Authors: Samuel, Benitha Wises, Mani, Gunaseelan, Ganesh, Purushothaman, Thabet, Sabri T. M., Kedim, Imed
Format: Article
Language:English
Subjects:
Fixed points (mathematics)
Fractional calculus
Fuzzy sets
Laplace transforms
Ordinary differential equations
Theorems
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Summary:In this article, we introduce a notion of controlled orthogonal δ ‐metric‐type spaces with an example. Further, we prove a contraction theorem and a generalized fixed point theorem in controlled orthogonal δ ‐metric‐type spaces. Finally, we illustrate two applications of the obtained fixed point results on the Atangana–Baleanu fractional integrals and the Riemann–Liouville fractional integrals. These applications showcase the versatility and efficacy of the developed theoretical framework in addressing real‐world mathematical problems.
ISSN:2314-8896
2314-8888
DOI:10.1155/jofs/5560159