111-LQP-JABS 20260903105656 Lumina Quest Publishing m.arslansohail@gmail.com Lumina Quest Publishing Journal of Advanced Biological Sciences J. Adv. Biol. Sci. 3134-8823 10.66590/jabs https://lquestpub.com/archives.php?journal=journal-of-advanced-biological-sciences 06 30 2026 06 30 2026 3 1 10.66590/jabs20260301 https://lquestpub.com/articles-list.php?journal=journal-of-advanced-biological-sciences&volume=3&issue=1 Differential Equations in the Modeling of Biological Systems: Advancing AI and Nanotechnology-Based Engineering Applications Ibtisam Mahmoub Osman Mohammed Sakina Ibrahim Ali Abonaib Background: Differential equations play a fundamental role in modeling dynamic biological systems; however, traditional approaches often face limitations in handling complex, nonlinear and multi-scale biological data. Objective: To develop and evaluate an integrated modeling framework combining differential equations, artificial intelligence and nanotechnology-based approaches for simulating and optimizing biological systems. Methods: This computational and analytical modeling study was conducted at Hail city mathematical models based on ordinary and partial differential equations were developed to represent biological processes, including cellular interactions and transport phenomena. Artificial intelligence techniques, including machine learning algorithms and Physics-Informed Neural Networks (PINNs), were applied for parameter optimization and model enhancement. Results: AI-integrated models demonstrated superior performance compared to traditional models, with higher predictive accuracy (R² up to 0.95) and lower error rates. PINNs showed the highest stability and fastest convergence. Sensitivity analysis identified diffusion coefficient and reaction rate as key determinants of system behavior. Nanotechnology modeling revealed that smaller particle size and higher diffusion rates significantly improved drug delivery efficiency and target site accumulation. Overall, the integrated framework enhanced model robustness and predictive capability. Conclusion: The integration of differential equations with artificial intelligence and nanotechnology provides a powerful and efficient approach for modeling complex biological systems. 06 30 2026 06 30 2026 13 18 10.66590/jabs2026030103 https://lquestpub.com/article/10.66590/jabs2026030103