Fractional Order Systems and Their Applications
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, an...
Wedi'i Gadw mewn:
| Fformat: | Online |
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| Iaith: | Saesneg |
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MDPI - Multidisciplinary Digital Publishing Institute
2025
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| Pynciau: | |
| Mynediad Ar-lein: | ONIX_20250220_9783725826803_386 |
| Tagiau: |
Dim Tagiau, Byddwch y cyntaf i dagio'r cofnod hwn!
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| _version_ | 1869516842194698240 |
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| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-153022 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1530222025-02-20T13:26:31Z Fractional Order Systems and Their Applications Lopes, António Chen, Liping Parrodo’paradox Mann iteration Julia set alternated system connectivity fuzzy fractional differential equations Caputo derivative fractional hyperbolic function strongly generalized Hukuhara differentiability Ulam-type stability Hermite–Hadamard inequality exponentially nonconvex function modified Fox–Wright function fractional integrals error estimation Leslie–Gower double Allee effect Hopf bifurcation global stability nonlocal operator Kalman filter state of charge fuzzy inference lithium-ion batteries Maglev system fractional order PID fractional order sliding mode fractional order fuzzy control GWO-PSO Liu process Caputo fuzzy fractional differential equations fuzzy process credibility space inverse problem spectral collocation method fractional diffusion fractional calculus fractional-order digital manufacturing supply chain synchronization control fractional-order system multi-agent guaranteed cost consensus delay-dependent ψ-Hilfer fractional derivative Riemann–Liouville fractional derivative Caputo fractional derivative system of fractional differential equations fractional-order Jerk system chaos hopf bifurcation stability time delay feedback controller fractional-order PDσ controller delayed linear fractional-order systems feedback controller positive invariant set asymptotic stabilization n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science 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. 2025-02-20T13:26:29Z 2025-02-20T13:26:29Z 2024 book ONIX_20250220_9783725826803_386 9783725826803 9783725826797 https://directory.doabooks.org/handle/20.500.12854/153022 eng application/octet-stream Attribution 4.0 International https://mdpi.com/books/pdfview/book/10252 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-7258-2679-7 10.3390/books978-3-7258-2679-7 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783725826803 9783725826797 264 Basel open access |
| spellingShingle | Parrodo’paradox Mann iteration Julia set alternated system connectivity fuzzy fractional differential equations Caputo derivative fractional hyperbolic function strongly generalized Hukuhara differentiability Ulam-type stability Hermite–Hadamard inequality exponentially nonconvex function modified Fox–Wright function fractional integrals error estimation Leslie–Gower double Allee effect Hopf bifurcation global stability nonlocal operator Kalman filter state of charge fuzzy inference lithium-ion batteries Maglev system fractional order PID fractional order sliding mode fractional order fuzzy control GWO-PSO Liu process Caputo fuzzy fractional differential equations fuzzy process credibility space inverse problem spectral collocation method fractional diffusion fractional calculus fractional-order digital manufacturing supply chain synchronization control fractional-order system multi-agent guaranteed cost consensus delay-dependent ψ-Hilfer fractional derivative Riemann–Liouville fractional derivative Caputo fractional derivative system of fractional differential equations fractional-order Jerk system chaos hopf bifurcation stability time delay feedback controller fractional-order PDσ controller delayed linear fractional-order systems feedback controller positive invariant set asymptotic stabilization n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science Fractional Order Systems and Their Applications |
| title | Fractional Order Systems and Their Applications |
| title_full | Fractional Order Systems and Their Applications |
| title_fullStr | Fractional Order Systems and Their Applications |
| title_full_unstemmed | Fractional Order Systems and Their Applications |
| title_short | Fractional Order Systems and Their Applications |
| title_sort | fractional order systems and their applications |
| topic | Parrodo’paradox Mann iteration Julia set alternated system connectivity fuzzy fractional differential equations Caputo derivative fractional hyperbolic function strongly generalized Hukuhara differentiability Ulam-type stability Hermite–Hadamard inequality exponentially nonconvex function modified Fox–Wright function fractional integrals error estimation Leslie–Gower double Allee effect Hopf bifurcation global stability nonlocal operator Kalman filter state of charge fuzzy inference lithium-ion batteries Maglev system fractional order PID fractional order sliding mode fractional order fuzzy control GWO-PSO Liu process Caputo fuzzy fractional differential equations fuzzy process credibility space inverse problem spectral collocation method fractional diffusion fractional calculus fractional-order digital manufacturing supply chain synchronization control fractional-order system multi-agent guaranteed cost consensus delay-dependent ψ-Hilfer fractional derivative Riemann–Liouville fractional derivative Caputo fractional derivative system of fractional differential equations fractional-order Jerk system chaos hopf bifurcation stability time delay feedback controller fractional-order PDσ controller delayed linear fractional-order systems feedback controller positive invariant set asymptotic stabilization n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| topic_facet | Parrodo’paradox Mann iteration Julia set alternated system connectivity fuzzy fractional differential equations Caputo derivative fractional hyperbolic function strongly generalized Hukuhara differentiability Ulam-type stability Hermite–Hadamard inequality exponentially nonconvex function modified Fox–Wright function fractional integrals error estimation Leslie–Gower double Allee effect Hopf bifurcation global stability nonlocal operator Kalman filter state of charge fuzzy inference lithium-ion batteries Maglev system fractional order PID fractional order sliding mode fractional order fuzzy control GWO-PSO Liu process Caputo fuzzy fractional differential equations fuzzy process credibility space inverse problem spectral collocation method fractional diffusion fractional calculus fractional-order digital manufacturing supply chain synchronization control fractional-order system multi-agent guaranteed cost consensus delay-dependent ψ-Hilfer fractional derivative Riemann–Liouville fractional derivative Caputo fractional derivative system of fractional differential equations fractional-order Jerk system chaos hopf bifurcation stability time delay feedback controller fractional-order PDσ controller delayed linear fractional-order systems feedback controller positive invariant set asymptotic stabilization n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| url | ONIX_20250220_9783725826803_386 |