Fractional Order Dynamical Systems: Modeling, Analysis, and Applications
DOI:
https://doi.org/10.29070/93yfyc58Keywords:
Fractional, Dynamical Systems, Modeling, ApplicationsAbstract
Fractional Order Dynamical Systems (FODS) provide scientists with an improved modeling method to analyze systems with memory effects and long-range dependencies as well as hereditary properties. Fractional order systems that use fractional derivatives create nonlocal connections between their elements to produce enhanced real-world observation results. The study investigates FODS theory by examining its complete scope which includes mathematical definitions and modeling properties and system deployment applications. The modeling employs FDEs written using Caputo and Riemann-Liouville derivatives to develop an expanded system description. The investigation analyzes stability criteria in addition to controllability and observability properties by extending conventional control approaches into fractional domains. The stability analysis demonstrates non-standard spectral properties and generalized eigenvalue conditions by using Mittag-Leffler functions. The frequency-domain analysis demonstrates that fractional order systems produce continuous phase variations with non-integer slope characteristics that lead to their valuable applications in control engineering and bioengineering and finance. The research explores FOPID controllers to evaluate robustness through stability and noise suppression performance improvement. The study presents examples of fractional order applications in electrical circuits and viscoelastic materials together with signal processing systems before its conclusion. The research demonstrates positive fractional calculus applications in modern system theory with potential new computational and applied mathematical studies.
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