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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.
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Keywords
- adaptive control
- anomalous diffusion
- audio signal processing
- Caputo derivative
- complexity
- Control
- cuckoo search
- diffusion-wave equation
- fourier transform
- fractional
- Fractional calculus
- fractional complex networks
- fractional derivative
- fractional-order system
- global optimization
- harmonic impact
- heavy-tailed distribution
- Hurst exponent
- impulses
- Laplace transform
- linear prediction
- long memory
- Magnetic Resonance Imaging
- mass absorption
- Meaning
- Mittag-Leffler function
- musical signal
- optimal randomness
- parameter
- PID
- pinning synchronization
- reaction–diffusion terms
- swarm-based search
- time series
- time-varying delays
Links
DOI: 10.3390/books978-3-03921-609-3Editions
