Fractional Dynamics Systems: Modeling, Forecasting, and Control

Dear Colleagues,

Fractional dynamics systems model systems with "memory" and long-range interdependence using fractional calculus, producing more precise forecasting and control models. They are used to represent intricate phenomena that integer-order models are unable to in a variety of domains, including biology, engineering, and finance. Designing controllers, evaluating system characteristics like stability and controllability, and creating underlying mathematical theories are all included in the study of these systems.

Modeling

• Memory and Hereditary Properties: Fractional-order models incorporate memory effects, meaning the current state of a system depends not only on its present conditions but also on its entire past history.
• Non-Local Features: These models are useful for systems with non-local features, such as those with long-range dependencies or effects.
• Examples: Applications include viscoelastic material modeling, signal processing, financial systems, and the spread of diseases like COVID-19.

Forecasting

• Accurate Predictions: By accounting for memory, these models can provide more accurate forecasts of future states in complex systems.
• Data-Driven Models: Techniques like Artificial Neural Networks (ANNs) have been used with fractional models to improve forecasting accuracy in systems like financial markets.
• Epidemiological Modeling: Fractional-order models have been used to forecast epidemic trends, such as the number of confirmed cases and deaths.

Control

• Model-Based Control: Researchers develop model-based control design methods specifically for systems described by fractional-order dynamics.
• Control Design: The control designs can be applied to both fractional- and integer-order controllers, which can then be implemented in real-world applications.
• Application Example: In one example, a fractional calculus problem was used to design a setpoint filter to control a furnace's temperature, helping to suppress overshooting.
• System Analysis: Traditional control concepts like stability, controllability, and observability are extended to fractional-order systems, which often have non-standard properties.

Prof. Dr. Seenith Sivasundaram
Dr. Devaraj Vivek
Prof. Dr. Carlo Bianca
Guest Editors

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