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Fractal Fract
Volume 9
Issue 11
10.3390/fractalfract9110730
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Fixed Points of Exponential-Type Contractions in Fuzzy Metric Spaces with Applications to Nonlinear Fractional Boundary Value Problems

by
Amjad E. Hamza
1,
Ali H. Tedjani
2,
Hayel N. Saleh
3,
Khaled Aldwoah
4,*,
Osman Osman
5,*,
Hicham Saber
1 and
Mohammed Messaoudi
2
1
Department of Mathematics, College of Sciences, University of Ha’il, Ha’il 55473, Saudi Arabia
2
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3
Department of Mathematics, Faculty of Applied Sciences, Taiz University, Taiz 6803, Yemen
4
Department of Mathematics, Faculty of Sciences, Islamic University of Madinah, Madinah 42351, Saudi Arabia
5
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Fractal Fract. 2025, 9(11), 730; https://doi.org/10.3390/fractalfract9110730
Submission received: 9 October 2025 / Revised: 4 November 2025 / Accepted: 8 November 2025 / Published: 11 November 2025
(This article belongs to the Special Issue Nonlinear Fractional Differential Equation and Fixed-Point Theory, 2nd Edition)
Versions Notes

Abstract

In this paper, we introduce the notion of fuzzy exponential contractions within the framework of fuzzy metric spaces. These mappings, which involve point-dependent exponential terms, are studied under the assumptions of either fuzzy continuity or the weaker condition of fuzzy Picard continuity. We establish corresponding existence and uniqueness theorems, and we further demonstrate the scope of the theory through illustrative examples and by applying it to prove an existence and uniqueness result for a class of nonlinear fractional differential equations.
Keywords: fuzzy metric spaces; fuzzy logic; fuzzy exponential contractions; fuzzy continuous and Picard continuous mappings; fixed point fuzzy metric spaces; fuzzy logic; fuzzy exponential contractions; fuzzy continuous and Picard continuous mappings; fixed point

Share and Cite

MDPI and ACS Style

Hamza, A.E.; Tedjani, A.H.; Saleh, H.N.; Aldwoah, K.; Osman, O.; Saber, H.; Messaoudi, M. Fixed Points of Exponential-Type Contractions in Fuzzy Metric Spaces with Applications to Nonlinear Fractional Boundary Value Problems. Fractal Fract. 2025, 9, 730. https://doi.org/10.3390/fractalfract9110730

AMA Style

Hamza AE, Tedjani AH, Saleh HN, Aldwoah K, Osman O, Saber H, Messaoudi M. Fixed Points of Exponential-Type Contractions in Fuzzy Metric Spaces with Applications to Nonlinear Fractional Boundary Value Problems. Fractal and Fractional. 2025; 9(11):730. https://doi.org/10.3390/fractalfract9110730

Chicago/Turabian Style

Hamza, Amjad E., Ali H. Tedjani, Hayel N. Saleh, Khaled Aldwoah, Osman Osman, Hicham Saber, and Mohammed Messaoudi. 2025. "Fixed Points of Exponential-Type Contractions in Fuzzy Metric Spaces with Applications to Nonlinear Fractional Boundary Value Problems" Fractal and Fractional 9, no. 11: 730. https://doi.org/10.3390/fractalfract9110730

APA Style

Hamza, A. E., Tedjani, A. H., Saleh, H. N., Aldwoah, K., Osman, O., Saber, H., & Messaoudi, M. (2025). Fixed Points of Exponential-Type Contractions in Fuzzy Metric Spaces with Applications to Nonlinear Fractional Boundary Value Problems. Fractal and Fractional, 9(11), 730. https://doi.org/10.3390/fractalfract9110730

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