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RESEARCH ARTICLE

Fractional-order modeling and hybrid optimization-based optimal control for sustainable computing systems

Oluwaseun Olumide Okundalaye1* ,  Necati Ozdemir2 ,  Adedowole Alimi1 ,  Adaraniwon Amos Olalekan3
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1 Department of Mathematical Sciences, Faculty of Science, Adekunle Ajasin University, Akungba- Akoko, Ondo State , Nigeria
2 Department of Mathematics, Faculty of Science and Arts, Balıkesir University, Balıkesir , Türkiye
3 Department of Mathematics and Statistics, Federal Polytechnic Ado-Ekiti, Ado-Ekiti, Ekiti State , Nigeria
JASMC, 026340002 https://doi.org/10.36922/JASMC026340002
Received: 17 August 2026 | Revised: 21 September 2026 | Accepted: 21 September 2026 | Published online: 21 October 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

The rapid growth of energy-intensive computing systems calls for intelligent resource-management strategies that simultaneously enhance energy efficiency, thermal stability, and quality of service. This work presents a hybrid fractional-order optimization framework for memory-dependent dynamics in sustainable and energy-aware computing systems. A four-state fractional-order model was developed using the Caputo fractional derivative to capture long-term temporal dependencies, cumulative thermal effects, and delayed system responses, with state variables comprising central processing unit (CPU) utilization, power consumption, system temperature, and workload queue length. The workload-demand and CPU-dynamics components of the model are calibrated against a pre-processed subset of the Google Cluster Trace 2019, comprising 8,064 samples at 300-s intervals over approximately 28 days of production data-center operation. Frequency-domain identification recovers a 12.00-h diurnal cycle in the workload, while least-squares fitting yields a unit steady-state gain (K = 0.9999) and a 300-second CPU time constant, both consistent with the physical properties of aggregated server workloads. A hybrid fractional-order particle swarm optimization (PSO) framework, integrating the global exploration of PSO with the local refinement of a fractional forward–backward sweep method based on Pontryagin’s Minimum Principle, is then applied to solve the resulting optimal control problem over a 100-s horizon. The framework is benchmarked against a Linear Quadratic Regulator and a Model Predictive Control scheme. Sensitivity analysis over the fractional order confirmed that the framework remains bounded and stable across the investigated range, with α acting as a tuning parameter for the trade-off between responsiveness and damping. These findings suggest that integrating fractional-order memory with hybrid optimization offers a promising route toward improved energy–performance–thermal trade-offs in green data centers, cloud and edge infrastructures, and energy-efficient high-performance computing systems.

Keywords
Sustainable computing
Energy-aware computing
Fractional-order modeling
Hybrid fractional particle swarm optimization
Optimal control
Energy efficiency
Resource management.
Funding
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
Conflict of interest
Oluwaseun Olumide Okundalaye is an Editorial Board Member of this journal, but was not in any way involved in the editorial and peer-review process conducted for this paper, directly or indirectly. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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