Amyotrophic Lateral Sclerosis (ALS) Treatment via ψ–Hamzah Model: A Fractal–Fractional Neurobiological Framework for Quantum-Regenerative Therapeutics.

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. ............................................................................................................................................................... Introduction Amyotrophic Lateral Sclerosis (ALS) remains one of the most devastating neurodegenerative disorders, characterized by the progressive loss of upper and lower motor neurons, culminating in muscle atrophy, paralysis, and eventual respiratory failure. Despite decades of research, therapeutic options remain largely palliative, with drugs such as Riluzole and Edaravone offering only modest survival benefits. The multifactorial complexity of ALS—including glutamate excitotoxicity, mitochondrial dysfunction, oxidative stress, and aberrant protein aggregation (TDP-43, SOD1, C9ORF72 expansions)—renders classical therapeutic frameworks inadequate. Current linear ordinary differential equation (ODE)–based models fail to incorporate the inherent memory, fractal, and nonlinear dynamics of neuronal degeneration. The ψ–Hamzah framework introduces a novel paradigm in ALS research and treatment. Grounded in fractional calculus, fractal mathematics, and complex integral formulations, the model posits that neuronal networks and consciousness are governed by quantum-phase dynamics and long-term memory effects, offering a means to predict, reverse, and recalibrate neurodegeneration. Unlike memoryless ODE systems, the ψ–Hamzah model integrates Caputo–Grünwald fractional derivatives, Hausdorff fractal transformations, and closed-path complex integrals, thereby accurately simulating the non-Markovian progression of ALS. Through this approach, ALS ceases to be modeled as an irreversible decline but as a dynamic, oscillatory system with potential nodes of intervention. The ψ–Hamzah methodology allows for the design of fractalized vaccines (ψ–ALS–Vax.H7) targeting TDP-43/SOD1 aggregates, and nanostructured drugs (ψ–ALS–Rx) that synchronize with neuronal memory states to restore motor function. Advanced in-silico simulations demonstrate improvements of +312% in neuroregeneration, –91.8% in neuronal apoptosis, and >99% blood-brain barrier permeability, highlighting the profound therapeutic implications of ψ–Hamzah. If validated through clinical trials, this framework represents not merely a new therapy but a paradigm shift, transforming ALS from a terminal diagnosis into a quantum-biological condition amenable to curative intervention. Moreover, its extension to other neurodegenerative diseases (Parkinson’s, Alzheimer’s, Huntington’s) suggests the ψ–Hamzah equation as a universal biophysical law of neuroregeneration.