Fractional Calculus and the Future of Science
Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientif...
Sábháilte in:
| Formáid: | Online |
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| Teanga: | Béarla |
| Foilsithe / Cruthaithe: |
MDPI - Multidisciplinary Digital Publishing Institute
2022
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| Ábhair: | |
| Rochtain ar líne: | ONIX_20220506_9783036528267_75 |
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Níl clibeanna ann, Bí ar an gcéad duine le clib a chur leis an taifead seo!
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| _version_ | 1869518662698795008 |
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| collection | Directory of Open Access Books |
| description | Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding. |
| format | Online |
| id | doab-20.500.12854ir-81009 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-810092024-03-28T03:32:17Z Fractional Calculus and the Future of Science West, Bruce J. fractional diffusion continuous time random walks reaction–diffusion equations reaction kinetics multidimensional scaling fractals fractional calculus financial indices entropy Dow Jones complex systems Skellam process subordination Lévy measure Poisson process of order k running average complexity chaos logistic differential equation liouville-caputo fractional derivative local discontinuous Galerkin methods stability estimate Mittag-Leffler functions Wright functions fractional relaxation diffusion-wave equation Laplace and Fourier transform fractional Poisson process complex systems distributed-order operators viscoelasticity transport processes control theory fractional order PID control PMSM frequency-domain control design optimal tuning Gaussian watermarks statistical assessment false positive rate semi-fragile watermarking system fractional dynamics fractional-order thinking heavytailedness big data machine learning variability diversity telegrapher’s equations fractional telegrapher’s equation continuous time random walk transport problems fractional conservations laws variable fractional model turbulent flows fractional PINN physics-informed learning n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding. 2022-05-06T11:21:28Z 2022-05-06T11:21:28Z 2022 book ONIX_20220506_9783036528267_75 9783036528267 9783036528274 https://directory.doabooks.org/handle/20.500.12854/81009 eng image/jpeg Attribution 4.0 International https://mdpi.com/books/pdfview/book/5351 https://mdpi.com/books/pdfview/book/5351 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-0365-2827-4 10.3390/books978-3-0365-2827-4 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783036528267 9783036528274 312 Basel open access |
| spellingShingle | fractional diffusion continuous time random walks reaction–diffusion equations reaction kinetics multidimensional scaling fractals fractional calculus financial indices entropy Dow Jones complex systems Skellam process subordination Lévy measure Poisson process of order k running average complexity chaos logistic differential equation liouville-caputo fractional derivative local discontinuous Galerkin methods stability estimate Mittag-Leffler functions Wright functions fractional relaxation diffusion-wave equation Laplace and Fourier transform fractional Poisson process complex systems distributed-order operators viscoelasticity transport processes control theory fractional order PID control PMSM frequency-domain control design optimal tuning Gaussian watermarks statistical assessment false positive rate semi-fragile watermarking system fractional dynamics fractional-order thinking heavytailedness big data machine learning variability diversity telegrapher’s equations fractional telegrapher’s equation continuous time random walk transport problems fractional conservations laws variable fractional model turbulent flows fractional PINN physics-informed learning n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science Fractional Calculus and the Future of Science |
| title | Fractional Calculus and the Future of Science |
| title_full | Fractional Calculus and the Future of Science |
| title_fullStr | Fractional Calculus and the Future of Science |
| title_full_unstemmed | Fractional Calculus and the Future of Science |
| title_short | Fractional Calculus and the Future of Science |
| title_sort | fractional calculus and the future of science |
| topic | fractional diffusion continuous time random walks reaction–diffusion equations reaction kinetics multidimensional scaling fractals fractional calculus financial indices entropy Dow Jones complex systems Skellam process subordination Lévy measure Poisson process of order k running average complexity chaos logistic differential equation liouville-caputo fractional derivative local discontinuous Galerkin methods stability estimate Mittag-Leffler functions Wright functions fractional relaxation diffusion-wave equation Laplace and Fourier transform fractional Poisson process complex systems distributed-order operators viscoelasticity transport processes control theory fractional order PID control PMSM frequency-domain control design optimal tuning Gaussian watermarks statistical assessment false positive rate semi-fragile watermarking system fractional dynamics fractional-order thinking heavytailedness big data machine learning variability diversity telegrapher’s equations fractional telegrapher’s equation continuous time random walk transport problems fractional conservations laws variable fractional model turbulent flows fractional PINN physics-informed learning n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| topic_facet | fractional diffusion continuous time random walks reaction–diffusion equations reaction kinetics multidimensional scaling fractals fractional calculus financial indices entropy Dow Jones complex systems Skellam process subordination Lévy measure Poisson process of order k running average complexity chaos logistic differential equation liouville-caputo fractional derivative local discontinuous Galerkin methods stability estimate Mittag-Leffler functions Wright functions fractional relaxation diffusion-wave equation Laplace and Fourier transform fractional Poisson process complex systems distributed-order operators viscoelasticity transport processes control theory fractional order PID control PMSM frequency-domain control design optimal tuning Gaussian watermarks statistical assessment false positive rate semi-fragile watermarking system fractional dynamics fractional-order thinking heavytailedness big data machine learning variability diversity telegrapher’s equations fractional telegrapher’s equation continuous time random walk transport problems fractional conservations laws variable fractional model turbulent flows fractional PINN physics-informed learning n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| url | ONIX_20220506_9783036528267_75 |