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Linear Fractional Diffusion-Wave Equation for Scientists and Engineers
This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Birkhäuser,
2015.
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| Edición: | 1st ed. 2015. |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-3-319-17954-4 | ||
| 003 | DE-He213 | ||
| 005 | 20220118154242.0 | ||
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| 008 | 150703s2015 sz | s |||| 0|eng d | ||
| 020 | |a 9783319179544 |9 978-3-319-17954-4 | ||
| 024 | 7 | |a 10.1007/978-3-319-17954-4 |2 doi | |
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| 100 | 1 | |a Povstenko, Yuriy. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Linear Fractional Diffusion-Wave Equation for Scientists and Engineers |h [electronic resource] / |c by Yuriy Povstenko. |
| 250 | |a 1st ed. 2015. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Birkhäuser, |c 2015. | |
| 300 | |a XIV, 460 p. 221 illus., 7 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 505 | 0 | |a 1.Introduction -- 2.Mathematical Preliminaries -- 3.Physical Backgrounds -- 4.Equations with one Space Variable in Cartesian Coordinates -- 5.Equations with one Space Variable in Polar Coordinates -- 6.Equations with one Space Variable in Spherical Coordinates -- 7.Equations with two Space Variables in Cartesian Coordinates -- 8.Equations in Polar Coordinates -- 9.Axisymmetric equations in Cylindrical Coordinates -- 10.Equations with three Space Variables in Cartesian Coordinates -- 11.Equations with three space Variables in Cylindrical Coordinates -- 12.Equations with three space Variables in Spherical Coordinates -- Conclusions -- Appendix: Integrals -- References. | |
| 520 | |a This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the "long-tail" power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier's, Fick's and Darcy's laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and fractals for graduate and postgraduate students. The volume will also serve as a valuable reference guide for specialists working in applied mathematics, physics, geophysics and the engineering sciences. | ||
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 1 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Mathematical Methods in Physics. |
| 650 | 2 | 4 | |a Mathematical Physics. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319179551 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319179537 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319373492 |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-17954-4 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||