Dual G-orbital contractions: Common fixed points and applications to fractional differential equations

Raweerote Suparatulatorn; Khuanchanok Chaichana; Phakdi Charoensawan; Raweerote Suparatulatorn; Khuanchanok Chaichana; Phakdi Charoensawan

doi:10.3934/math.20261270

AIMS Mathematics

2026, Volume 11, Issue 10: 32318-32346. doi: 10.3934/math.20261270

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Dual G-orbital contractions: Common fixed points and applications to fractional differential equations

1.
Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
2.
Department of Mathematics, Faculty of Science, Lampang Rajabhat University, Lampang 52100, Thailand
3.
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
4.
Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand

Received: 28 July 2026 Revised: 08 September 2026 Accepted: 10 September 2026 Published: 08 October 2026
MSC : 47H09, 47H10, 54H25

In this paper, we introduce the novel concept of dual $ G $-orbital $ \alpha $-$ R $-contractions for mapping pairs in $ b $-metric spaces endowed with a directed graph. By employing the dual $ G $-orbital transitive property alongside Property (E), we derive new existence and uniqueness theorems for common fixed points. To validate our theoretical results, we provide a concrete numerical example that demonstrates the computation of such points. Furthermore, we illustrate the applicability of our mathematical framework by proving the existence of a common solution to a system of nonlinear fractional differential equations involving Caputo fractional derivatives and nonlocal integral boundary conditions.
- common fixed point,
- $ b $-metric space,
- directed graph,
- $ G $-orbital,
- dual connected-image contractions,
- fractional differential equations
Citation: Raweerote Suparatulatorn, Khuanchanok Chaichana, Phakdi Charoensawan. Dual G-orbital contractions: Common fixed points and applications to fractional differential equations[J]. AIMS Mathematics, 2026, 11(10): 32318-32346. doi: 10.3934/math.20261270

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Abstract

In this paper, we introduce the novel concept of dual $ G $-orbital $ \alpha $-$ R $-contractions for mapping pairs in $ b $-metric spaces endowed with a directed graph. By employing the dual $ G $-orbital transitive property alongside Property (E), we derive new existence and uniqueness theorems for common fixed points. To validate our theoretical results, we provide a concrete numerical example that demonstrates the computation of such points. Furthermore, we illustrate the applicability of our mathematical framework by proving the existence of a common solution to a system of nonlinear fractional differential equations involving Caputo fractional derivatives and nonlocal integral boundary conditions.

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