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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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
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Fixed points (mathematics)
Fractional calculus
Fuzzy sets
Laplace transforms
Ordinary differential equations
Theorems
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Mani, Gunaseelan
Ganesh, Purushothaman
Thabet, Sabri T. M.
Kedim, Imed
description 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.
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subjects Fixed points (mathematics)
Fractional calculus
Fuzzy sets
Laplace transforms
Ordinary differential equations
Theorems
title Fixed Point Theorems on Controlled Orthogonal δ ‐Metric‐Type Spaces and Applications to Fractional Integrals
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