Fractional Order Systems and Their Applications

• Format: eBook
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2024
• Subjects: alternated system; asymptotic stabilization; Caputo derivative; Caputo fractional derivative; Caputo fuzzy fractional differential equations; chaos; connectivity; control; credibility space; delay-dependent; delayed linear fractional-order systems; digital manufacturing; double Allee effect; error estimation; exponentially nonconvex function; feedback controller; fractional calculus; fractional diffusion; fractional hyperbolic function; fractional integrals; fractional order fuzzy control; fractional order PID; fractional order sliding mode; fractional-order; fractional-order Jerk system; fractional-order PDσ controller; fractional-order system; fuzzy fractional differential equations; fuzzy inference; fuzzy process; global stability; guaranteed cost consensus; GWO-PSO; Hermite–Hadamard inequality; Hopf bifurcation; inverse problem; Julia set; Kalman filter; Leslie–Gower; lithium-ion batteries; Liu process; Maglev system; Mann iteration; Mathematics and Science; modified Fox–Wright function; multi-agent; n/a; nonlocal operator; Parrodo’paradox; positive invariant set; Reference, Information and Interdisciplinary subjects; Research and information: general; Riemann–Liouville fractional derivative; spectral collocation method; stability; state of charge; strongly generalized Hukuhara differentiability; supply chain; synchronization; system of fractional differential equations; time delay feedback controller; Ulam-type stability; ψ-Hilfer fractional derivative
• ISBN: 9783725826803; 372582679X; 9783725826797; 3725826803
• DOI: 10.3390/books978-3-7258-2679-7

Fractional calculus (FC) generalizes the concepts of derivative and integral orders to non-integer orders. It was introduced by Leibniz (1646–1716) but remained a purely mathematical exercise for a long time, despite the original contributions to the field of important mathematicians, physicists, and engineers. FC has experienced rapid development in recent decades, both in mathematics and applied sciences, being recognized as an excellent tool to describe complex dynamics. Based on this, several models governing physical phenomena in the areas of science and engineering have been reformulated in light of FC for them to better reflecting their non-local and frequency- and history-dependent properties. Applications of FC include modeling of diffusion, viscoelasticity, and relaxation processes in fluid mechanics; the dynamics of mechanical, electronic, and biological systems; and signal processing and control. This reprint compiles articles from the Special Issue “Fractional Order Systems and Their Applications”, which focused on original and new research results on modeling and control of fractional order systems with applications in science and engineering. It includes 13 manuscripts addressing novel issues and specific topics that illustrate the richness and applicability of fractional calculus.