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Linear fractional diffusion-wave equation for scientists and engineers[electronic resource] /

纪录类型:	书目-语言数据,印刷品 : Monograph/item
[NT 15000414] null:	515.353
[NT 47271] Title/Author:	Linear fractional diffusion-wave equation for scientists and engineers/ by Yuriy Povstenko.
作者:	Povstenko, Yuriy.
出版者:	Cham : : Springer International Publishing :, 2015.
面页册数:	xiv, 460 p. : : ill. (some col.), digital ;; 24 cm.
Contained By:	Springer eBooks
标题:	Mathematical physics.
标题:	Mathematics.
标题:	Partial Differential Equations.
标题:	Mathematical Methods in Physics.
标题:	Mathematical Applications in the Physical Sciences.
标题:	Heat equation.
ISBN:	9783319179544 (electronic bk.)
ISBN:	9783319179537 (paper)
[NT 15000228] null:	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.
[NT 15000229] null:	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.
电子资源:	http://dx.doi.org/10.1007/978-3-319-17954-4

Linear fractional diffusion-wave equation for scientists and engineers[electronic resource] /
Povstenko, Yuriy.

Linear fractional diffusion-wave equation for scientists and engineers[electronic resource] /by Yuriy Povstenko. - Cham :Springer International Publishing :2015. - xiv, 460 p. :ill. (some col.), digital ;24 cm.

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.

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.

ISBN: 9783319179544 (electronic bk.)

Standard No.: 10.1007/978-3-319-17954-4doiSubjects--Topical Terms:

182314
Mathematical physics.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Linear fractional diffusion-wave equation for scientists and engineers[electronic resource] /
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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.
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