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Linear fractional diffusion-wave equ...

Povstenko, Yuriy,

Linear fractional diffusion-wave equation for scientists and engineers /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Linear fractional diffusion-wave equation for scientists and engineers /Yuriy Povstenko.
作者:	Povstenko, Yuriy,
出版者:	Cham :Birkhäuser,c2015.
面頁冊數:	xiv, 460 p. :ill. (some col.) ;24 cm.
標題:	Heat equation.
ISBN:	3319179535

Linear fractional diffusion-wave equation for scientists and engineers /
Povstenko, Yuriy,

Linear fractional diffusion-wave equation for scientists and engineers /Yuriy Povstenko. - Cham :Birkhäuser,c2015. - xiv, 460 p. :ill. (some col.) ;24 cm.

Includes bibliographical references (p. 445-460).

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: 3319179535

LCCN: 2015944697Subjects--Topical Terms:

224254
Heat equation.

LC Class. No.: QA377 / .P68 2015

Dewey Class. No.: 530.1/24

Linear fractional diffusion-wave equation for scientists and engineers /
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010 $a 2015944697
020 $a 3319179535
020 $a 9783319179537 : $c NT$3069
020 $z 9783319179544 (eBook)
035 $a (OCoLC)905638835
035 $a ocn905638835
040 $a YDXCP $b eng $c YDXCP $d BTCTA $d CDX $d MUU $d OCLCF $d S4S
050 4 $a QA377 $b .P68 2015
082 0 4 $a 530.1/24 $2 23
100 1 $a Povstenko, Yuriy, $e author. $3 735571
245 1 0 $a Linear fractional diffusion-wave equation for scientists and engineers / $c Yuriy Povstenko.
260 $a Cham : $b Birkhäuser, $c c2015.
300 $a xiv, 460 p. : $b ill. (some col.) ; $c 24 cm.
504 $a Includes bibliographical references (p. 445-460).
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 Heat equation. $3 224254
650 0 $a Mathematical physics. $3 190854