Modeling and Control of Fractal and Fractional Dynamical Systems in Neurological Disorders

Dear Colleagues,

Neurological disorders are considered to be complex affections from both clinical and mathematical perspectives. That is why mathematics and engineering have been trying for some time to contribute to objectively revealing the non-apparent characteristics of this type of disease. Finding suitable models has become more and more challenging, and “non-conventional” dynamical structures must be used. It is in this sense that fractional and fractal dynamics appear to provide alternative techniques to address such intricate and long-suffering diseases; not only for patients, but also for caregivers. 

Neurological disorders are diseases of the central and peripheral nervous systems. Among the neurological diseases considered by the World Health Organization (WHO), this Special Issue will also focus on typical complex affections that include seizure and degenerative disorders.

Examples of neurodegenerative illnesses are as follows:

• Alzheimer's disease (D).
• Dementias (D).
• Mental disorders (schizophrenia, autism spectrum disorder (ASD), and attention deficit hyperactivity disorder (ADHD)) (D).
• Parkinson's and other movement disorders (D).

These affections are traditionally seen as complex from clinical and mathematical perspectives. As such, increasingly complex algorithms have been proposed to reflect more of the underlying dynamics of these conditions, but only recently have they been considered from fractal or fractional dynamics viewpoints. Moreover, some of them still remain unexplored by these techniques.

As a consequence of the shortage of fractal and fractional dynamical models to investigate the complex diseases described above, we encourage the scientific community to participate in our novel Special Issue, providing contributions on: Fractional dynamical systems-based modeling and control:

• Linear/Nonlinear deterministic dynamical models.
• Stochastic ordinary/partial differential equation-based models.
• Stability, controllability, and observability.
• PID, optimal, and other fractional control techniques.
• Fractional neural networks.

Fractal dynamics perspectives:

• Fractal analysis of time series.
• Fractal geometry.
• Numerical issues.
• Hurst exponent and predictability. Fractal artificial intelligence (Fractal AI).
• Multifractal analysis.
• Entropy analysis.

Dr. Ricardo Zavala-Yoé
Dr. Jorge Mario Cruz-Duarte
Prof. Dr. Porfirio Toledo Hernández
Guest Editors

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• neurological disorders
• fractal analysis
• entropy applications
• neurological disorders
• fractional dynamical systems