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...
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Springer
2016
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| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/59972 |
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oai:scholar.dlu.edu.vn:DLU123456789-599722023-11-11T06:58:29Z Linear Fractional Diffusion-Wave Equation for Scientists and Engineers Povstenko, Yuriy Calculus Mathematics Mathematical physics Heat equation 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. 2016-04-01T02:24:30Z 2016-04-01T02:24:30Z 2015 Book 978-3-319-17954-4 978-3-319-17953-7 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/59972 en application/pdf Springer |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
Calculus Mathematics Mathematical physics Heat equation |
| spellingShingle |
Calculus Mathematics Mathematical physics Heat equation Povstenko, Yuriy Linear Fractional Diffusion-Wave Equation for Scientists and Engineers |
| description |
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. |
| format |
Book |
| author |
Povstenko, Yuriy |
| author_facet |
Povstenko, Yuriy |
| author_sort |
Povstenko, Yuriy |
| title |
Linear Fractional Diffusion-Wave Equation for Scientists and Engineers |
| title_short |
Linear Fractional Diffusion-Wave Equation for Scientists and Engineers |
| title_full |
Linear Fractional Diffusion-Wave Equation for Scientists and Engineers |
| title_fullStr |
Linear Fractional Diffusion-Wave Equation for Scientists and Engineers |
| title_full_unstemmed |
Linear Fractional Diffusion-Wave Equation for Scientists and Engineers |
| title_sort |
linear fractional diffusion-wave equation for scientists and engineers |
| publisher |
Springer |
| publishDate |
2016 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/59972 |
| _version_ |
1782544451123544064 |