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Volume 9
Issue 8
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Article

Novel Fixed Point Results in Rectangular Gb-Metric Spaces and Some Applications on Fractional Differential Equations

by
Rende Ramadan
1,
Ozgur Ege
2,* and
Rajagopalan Ramaswamy
3,*
1
Natural Science Institute, Ege University, Bornova 35100, Izmir, Turkey
2
Department of Mathematics, Ege University, Bornova 35100, Izmir, Turkey
3
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Fractal Fract. 2025, 9(8), 527; https://doi.org/10.3390/fractalfract9080527
Submission received: 26 June 2025 / Revised: 29 July 2025 / Accepted: 11 August 2025 / Published: 13 August 2025
(This article belongs to the Special Issue Nonlinear Fractional Differential Equation and Fixed-Point Theory, 2nd Edition)
Versions Notes

Abstract

In this work, we prove some fixed point theorems in rectangular Gb-metric space, which is the generalization of rectangular metric space and Gb-metric space. Moreover, we give some examples to support our theoretical findings. Finally, using our main results, we present some applications to obtain solutions of Riemann–Liouville and Atangana–Baleanu fractional integral equations.
Keywords: fixed point; Gb-metric; fractional differential equations fixed point; Gb-metric; fractional differential equations

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MDPI and ACS Style

Ramadan, R.; Ege, O.; Ramaswamy, R. Novel Fixed Point Results in Rectangular Gb-Metric Spaces and Some Applications on Fractional Differential Equations. Fractal Fract. 2025, 9, 527. https://doi.org/10.3390/fractalfract9080527

AMA Style

Ramadan R, Ege O, Ramaswamy R. Novel Fixed Point Results in Rectangular Gb-Metric Spaces and Some Applications on Fractional Differential Equations. Fractal and Fractional. 2025; 9(8):527. https://doi.org/10.3390/fractalfract9080527

Chicago/Turabian Style

Ramadan, Rende, Ozgur Ege, and Rajagopalan Ramaswamy. 2025. "Novel Fixed Point Results in Rectangular Gb-Metric Spaces and Some Applications on Fractional Differential Equations" Fractal and Fractional 9, no. 8: 527. https://doi.org/10.3390/fractalfract9080527

APA Style

Ramadan, R., Ege, O., & Ramaswamy, R. (2025). Novel Fixed Point Results in Rectangular Gb-Metric Spaces and Some Applications on Fractional Differential Equations. Fractal and Fractional, 9(8), 527. https://doi.org/10.3390/fractalfract9080527

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