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<p>This paper develops a heterogeneous Atangana–Baleanu fractional-order framework to model malware diffusion in multi-cloud environments, incorporating stochastic perturbations to represent ambient cyber noise. A twelve-compartment Malware Propagation in Multi-Cloud Environments (MMCE) topology is formulated to distinguish sector-specific infection classes, quarantine layers, traced nodes, and protection strata. By assigning distinct fractional orders to each compartment, the model captures compartment-dependent hereditary memory effects and anomalous temporal persistence. Within this framework, both deterministic and stochastic optimal control problems are formulated to minimize the cumulative infection burden and intervention costs in the presence of Brownian perturbations. The existence, uniqueness, and Ulam–Hyers stability of the resulting fractional dynamical systems are rigorously established under standard Lipschitz continuity conditions. Moreover, the associated Pontryagin-type optimality systems are analytically derived within the Atangana–Baleanu fractional setting, providing a mathematically consistent foundation for subsequent numerical implementation. Theoretical results indicate that heterogeneous memory effects and stochastic forcing play a significant role in shaping the structure and stability of optimal control strategies. Consequently, the proposed framework offers a rigorous and flexible platform for future computational investigations and for the development of memory-aware, resilience-oriented mitigation policies in multi-cloud cyber ecosystems.</p>

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Stochastic optimal control of malware propagation in multi-cloud systems via heterogeneous Atangana–Baleanu fractional dynamics under Brownian motion

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月22日

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  • A. M. Sayed Ahmed,
  • Hamdy M. Ahmed

摘要

This paper develops a heterogeneous Atangana–Baleanu fractional-order framework to model malware diffusion in multi-cloud environments, incorporating stochastic perturbations to represent ambient cyber noise. A twelve-compartment Malware Propagation in Multi-Cloud Environments (MMCE) topology is formulated to distinguish sector-specific infection classes, quarantine layers, traced nodes, and protection strata. By assigning distinct fractional orders to each compartment, the model captures compartment-dependent hereditary memory effects and anomalous temporal persistence. Within this framework, both deterministic and stochastic optimal control problems are formulated to minimize the cumulative infection burden and intervention costs in the presence of Brownian perturbations. The existence, uniqueness, and Ulam–Hyers stability of the resulting fractional dynamical systems are rigorously established under standard Lipschitz continuity conditions. Moreover, the associated Pontryagin-type optimality systems are analytically derived within the Atangana–Baleanu fractional setting, providing a mathematically consistent foundation for subsequent numerical implementation. Theoretical results indicate that heterogeneous memory effects and stochastic forcing play a significant role in shaping the structure and stability of optimal control strategies. Consequently, the proposed framework offers a rigorous and flexible platform for future computational investigations and for the development of memory-aware, resilience-oriented mitigation policies in multi-cloud cyber ecosystems.