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Mathematics
Volume 14
Issue 2
10.3390/math14020262
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Two Types of Proximal Connected-Image Contractions in b-Metric Spaces and Applications to Fractional Differential Models

by
Khuanchanok Chaichana
1,2,3,
Ben Wongsaijai
1,2,3,*,
Adsadang Himakalasa
2 and
Phakdi Charoensawan
1,2,3,*
1
Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
2
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
3
Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand
*
Authors to whom correspondence should be addressed.
Mathematics 2026, 14(2), 262; https://doi.org/10.3390/math14020262
Submission received: 17 December 2025 / Revised: 6 January 2026 / Accepted: 7 January 2026 / Published: 9 January 2026
(This article belongs to the Special Issue Advanced Theoretical and Numerical Methods for Fractional Differential and Difference Equations)
Versions Notes

Abstract

In this paper, we introduce a new class of proximal connected-image contractions in the framework of b-metric spaces endowed with a directed graph. By employing auxiliary functions, we establish several existence and uniqueness results for best proximity points and fixed points under appropriate contractive conditions. To demonstrate the applicability of our theoretical findings, we apply the main results to a class of fractional differential equations, showing the effectiveness of the proposed approach.
Keywords: proximal connected-image contraction; fixed point theorem; b-metric space; fractional differential equation proximal connected-image contraction; fixed point theorem; b-metric space; fractional differential equation

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MDPI and ACS Style

Chaichana, K.; Wongsaijai, B.; Himakalasa, A.; Charoensawan, P. Two Types of Proximal Connected-Image Contractions in b-Metric Spaces and Applications to Fractional Differential Models. Mathematics 2026, 14, 262. https://doi.org/10.3390/math14020262

AMA Style

Chaichana K, Wongsaijai B, Himakalasa A, Charoensawan P. Two Types of Proximal Connected-Image Contractions in b-Metric Spaces and Applications to Fractional Differential Models. Mathematics. 2026; 14(2):262. https://doi.org/10.3390/math14020262

Chicago/Turabian Style

Chaichana, Khuanchanok, Ben Wongsaijai, Adsadang Himakalasa, and Phakdi Charoensawan. 2026. "Two Types of Proximal Connected-Image Contractions in b-Metric Spaces and Applications to Fractional Differential Models" Mathematics 14, no. 2: 262. https://doi.org/10.3390/math14020262

APA Style

Chaichana, K., Wongsaijai, B., Himakalasa, A., & Charoensawan, P. (2026). Two Types of Proximal Connected-Image Contractions in b-Metric Spaces and Applications to Fractional Differential Models. Mathematics, 14(2), 262. https://doi.org/10.3390/math14020262

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