Modeling and stability analysis of a memory-driven fractional labor dynamics system

Arusamy Mohanapriya; Nallappan Gunasekaran; Mostafa Fazly; Vadivel Rajarathinam; Arusamy Mohanapriya; Nallappan Gunasekaran; Mostafa Fazly; Vadivel Rajarathinam

doi:10.3934/era.2026105

Electronic Research Archive

2026, Volume 34, Issue 4: 2321-2347. doi: 10.3934/era.2026105

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Modeling and stability analysis of a memory-driven fractional labor dynamics system

1.
Department of Science and Humanities, S-VYASA University, Bengaluru, Karnadaka 560059, India
2.
Department of Natural Science, Eastern Michigan Joint College of Engineering, Beibu Gulf University, Qinzhou 535011, China
3.
Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
4.
Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, Thailand

Received: 20 December 2025 Revised: 17 February 2026 Accepted: 03 March 2026 Published: 16 March 2026

This paper investigates the existence and stability of a fractional-order labor dynamics model formulated using the fractional Nabla difference operator, specifically the Atangana-Baleanu fractional derivative in the Caputo sense. The model incorporates fractional dynamics to capture memory effects and the complex interactions associated with workforce layoffs. First, we present the mathematical formulation of the system and discuss its relevance to labor dynamics. Using the fixed-point theory, we establish the existence and uniqueness of solutions, demonstrating that the system is well posed. Furthermore, we examine the stability of the model in the Mittag-Leffler-Hyers-Ulam sense, providing insight into its long-term qualitative behavior. Numerical simulations support the theoretical findings and demonstrate that the fractional-order parameter significantly influences the system's dynamics. Overall, this study offers a more general and flexible framework for modeling layoff processes using fractional calculus.
- fractional-order model,
- Atangana-Baleanu derivative,
- fractional Nabla difference operator,
- Mittag-Leffler-Hyers-Ulam stability
Citation: Arusamy Mohanapriya, Nallappan Gunasekaran, Mostafa Fazly, Vadivel Rajarathinam. Modeling and stability analysis of a memory-driven fractional labor dynamics system[J]. Electronic Research Archive, 2026, 34(4): 2321-2347. doi: 10.3934/era.2026105

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Abstract

This paper investigates the existence and stability of a fractional-order labor dynamics model formulated using the fractional Nabla difference operator, specifically the Atangana-Baleanu fractional derivative in the Caputo sense. The model incorporates fractional dynamics to capture memory effects and the complex interactions associated with workforce layoffs. First, we present the mathematical formulation of the system and discuss its relevance to labor dynamics. Using the fixed-point theory, we establish the existence and uniqueness of solutions, demonstrating that the system is well posed. Furthermore, we examine the stability of the model in the Mittag-Leffler-Hyers-Ulam sense, providing insight into its long-term qualitative behavior. Numerical simulations support the theoretical findings and demonstrate that the fractional-order parameter significantly influences the system's dynamics. Overall, this study offers a more general and flexible framework for modeling layoff processes using fractional calculus.

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