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<p>When real-world systems like sensor networks or controllers face small disturbances, do their discrete fractional models stay reliable? We tackle this for a critical but unstudied problem: discrete delta fractional equations with summation multipoint boundary conditions (SMBCs). First, we build the mathematical foundation—the Green’s function—to prove solutions exist and are unique under Lipschitz conditions. Crucially, we show these solutions are Ulam–Hyers–Rassias stable: even when perturbed, they stay close to the true solution, with explicit guarantees for both uniform and varying disturbances. Testing this on a nonlinear system and a thermal sensor model confirms real-world resilience. This work bridges abstract fractional calculus with engineering robustness, giving designers confidence to deploy these models in next-generation technologies.</p>

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Stability analysis of discrete delta fractional models under summation multipoint constraints for robust engineering systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月3日

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  • Pshtiwan Othman Mohammed,
  • Eman Al-Sarairah,
  • Dumitru Baleanu,
  • Majeed Ahmad Yousif,
  • Meraa Arab

摘要

When real-world systems like sensor networks or controllers face small disturbances, do their discrete fractional models stay reliable? We tackle this for a critical but unstudied problem: discrete delta fractional equations with summation multipoint boundary conditions (SMBCs). First, we build the mathematical foundation—the Green’s function—to prove solutions exist and are unique under Lipschitz conditions. Crucially, we show these solutions are Ulam–Hyers–Rassias stable: even when perturbed, they stay close to the true solution, with explicit guarantees for both uniform and varying disturbances. Testing this on a nonlinear system and a thermal sensor model confirms real-world resilience. This work bridges abstract fractional calculus with engineering robustness, giving designers confidence to deploy these models in next-generation technologies.