Maxwell's Equation vs. Hamzah Equation: Superiority Analysis.

All Articles are Available: Orcid ID: https://orcid.org/my-orcid?orcid=0009-0009-3175-8563 Science Open ID: https://www.scienceopen.com/user/2c98a8bc-b8bb-49b3-9c91-2f2986a7e16e Safe Creative register the work titled "The Theory of Intelligent Evolution, the Hamzah Equation, and the Quantum Civilisation". Safe Creative registration #2504151474836. .................................................................................................................................................................................................. This paper presents a comprehensive comparative analysis between the classical Maxwell equations and the ψ–Hamzah model, highlighting the superiority of the latter in a range of scientific and interdisciplinary applications. The classical Maxwell equations, grounded in linear field dynamics, fail to account for memory effects and non-local interactions, which are critical in modeling complex, chaotic, and biological systems. In contrast, the ψ–Hamzah model introduces a revolutionary framework that incorporates memory-based field dynamics, fractional derivatives, and fractal time structures (ψ-time), offering a more accurate and flexible approach to field theory. The paper details the foundational differences between these models, showcasing how the ψ–Hamzah model enables the description of phenomena such as quantum information systems, neural signaling, and cosmic events, all of which lie beyond the reach of classical Maxwell equations. The study further highlights the model's robustness in handling non-ideal boundary conditions, chaotic systems, and its application in neurophysics, quantum cosmology, complex economics, and computational neuroscience. Through rigorous numerical, conceptual, and interdisciplinary analyses, we demonstrate that the ψ–Hamzah model not only surpasses Maxwell's equations in predictive accuracy and stability but also opens new frontiers in understanding electromagnetic fields, quantum dynamics, and interwoven systems across science. The paper concludes that the ψ–Hamzah model offers a superior and more adaptable framework for addressing modern challenges in both theoretical and applied physics.