Fractional Mathematical Modelling
This Reprint presents recent advances in fractional calculus, organized into three main themes: theoretical developments, methodological advances, and applications. Theoretical contributions examine two forms of the Riemann–Liouville derivative and their impact on solution structures, and introduce...
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| Format: | Online |
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| Jezik: | engleski |
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MDPI - Multidisciplinary Digital Publishing Institute
2026
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| Online pristup: | ONIX_20260416T142754_9783725855117_50 |
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| _version_ | 1869517475812474880 |
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| collection | Directory of Open Access Books |
| description | This Reprint presents recent advances in fractional calculus, organized into three main themes: theoretical developments, methodological advances, and applications. Theoretical contributions examine two forms of the Riemann–Liouville derivative and their impact on solution structures, and introduce anomalous diffusion models based on regularized general fractional derivatives with Sonin kernels. Methodological studies focus on improved analytical and numerical approaches, including the optimal q-Homotopy Analysis Method, iterative and perturbation techniques for nonlinear equations, and applications of the fractional differential quadrature method to nonlinear and high-dimensional systems. Applications demonstrate the breadth of fractional modeling, covering fuzzy systems and controllability, fractional-order boost converters, viscoelastic dampers, ZnO nanostructures, solar-cell charge dynamics, and personalized fractional-order controllers for anaesthesia. Together, these works highlight how fractional calculus continues to advance through theoretical developments, methodological advances, and practical applications across science, engineering, and medicine. |
| format | Online |
| id | doab-20.500.12854ir-174895 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2026 |
| publishDateRange | 2026 |
| publishDateSort | 2026 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1748952026-04-16T17:13:04Z Fractional Mathematical Modelling Rabiei, Faranak Kim, Dongwook Ali, Zeeshan Fractional differential equations Fractional integral equations Fractional calculus Anomalous diffusion Fuzzy fractional systems Riemann-Liouville derivatives Caputo-Fabrizio derivatives Hilfer operators Burger-Fisher equations Abel differential equations Riccati systems Lorenz systems Numerical methods Homotopy analysis Iterative methods Stability analysis Controllability Computational mathematics Viscoelastic dampers Nonlinear optical behavior ZnO nanostructures Solar cell modeling Biomedical control systems Anaesthesia autotuning Applications in science and engineering thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general This Reprint presents recent advances in fractional calculus, organized into three main themes: theoretical developments, methodological advances, and applications. Theoretical contributions examine two forms of the Riemann–Liouville derivative and their impact on solution structures, and introduce anomalous diffusion models based on regularized general fractional derivatives with Sonin kernels. Methodological studies focus on improved analytical and numerical approaches, including the optimal q-Homotopy Analysis Method, iterative and perturbation techniques for nonlinear equations, and applications of the fractional differential quadrature method to nonlinear and high-dimensional systems. Applications demonstrate the breadth of fractional modeling, covering fuzzy systems and controllability, fractional-order boost converters, viscoelastic dampers, ZnO nanostructures, solar-cell charge dynamics, and personalized fractional-order controllers for anaesthesia. Together, these works highlight how fractional calculus continues to advance through theoretical developments, methodological advances, and practical applications across science, engineering, and medicine. 2026-04-16T17:12:53Z 2026-04-16T17:12:53Z 2025 book ONIX_20260416T142754_9783725855117_50 9783725855117 9783725855124 https://directory.doabooks.org/handle/20.500.12854/174895 eng application/octet-stream Attribution 4.0 International https://mdpi.com/books/ https://mdpi.com/books/pdfview/book/11776 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-7258-5512-4 10.3390/books978-3-7258-5512-4 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783725855117 9783725855124 262 CH open access |
| spellingShingle | Fractional differential equations Fractional integral equations Fractional calculus Anomalous diffusion Fuzzy fractional systems Riemann-Liouville derivatives Caputo-Fabrizio derivatives Hilfer operators Burger-Fisher equations Abel differential equations Riccati systems Lorenz systems Numerical methods Homotopy analysis Iterative methods Stability analysis Controllability Computational mathematics Viscoelastic dampers Nonlinear optical behavior ZnO nanostructures Solar cell modeling Biomedical control systems Anaesthesia autotuning Applications in science and engineering thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general Fractional Mathematical Modelling |
| title | Fractional Mathematical Modelling |
| title_full | Fractional Mathematical Modelling |
| title_fullStr | Fractional Mathematical Modelling |
| title_full_unstemmed | Fractional Mathematical Modelling |
| title_short | Fractional Mathematical Modelling |
| title_sort | fractional mathematical modelling |
| topic | Fractional differential equations Fractional integral equations Fractional calculus Anomalous diffusion Fuzzy fractional systems Riemann-Liouville derivatives Caputo-Fabrizio derivatives Hilfer operators Burger-Fisher equations Abel differential equations Riccati systems Lorenz systems Numerical methods Homotopy analysis Iterative methods Stability analysis Controllability Computational mathematics Viscoelastic dampers Nonlinear optical behavior ZnO nanostructures Solar cell modeling Biomedical control systems Anaesthesia autotuning Applications in science and engineering thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general |
| topic_facet | Fractional differential equations Fractional integral equations Fractional calculus Anomalous diffusion Fuzzy fractional systems Riemann-Liouville derivatives Caputo-Fabrizio derivatives Hilfer operators Burger-Fisher equations Abel differential equations Riccati systems Lorenz systems Numerical methods Homotopy analysis Iterative methods Stability analysis Controllability Computational mathematics Viscoelastic dampers Nonlinear optical behavior ZnO nanostructures Solar cell modeling Biomedical control systems Anaesthesia autotuning Applications in science and engineering thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general |
| url | ONIX_20260416T142754_9783725855117_50 |