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Linear Fractional Diffusion-Wave Equation for Scientists and Engineers

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Linear Fractional Diffusion-Wave Equation for Scientists and Engineers/ by Yuriy Povstenko.
Author:	Povstenko, Yuriy.
Description:	XIV, 460 p. 221 illus., 7 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Partial differential equations. -
Online resource:	https://doi.org/10.1007/978-3-319-17954-4
ISBN:	9783319179544

Linear Fractional Diffusion-Wave Equation for Scientists and Engineers
Povstenko, Yuriy.

Linear Fractional Diffusion-Wave Equation for Scientists and Engineers[electronic resource] /by Yuriy Povstenko. - 1st ed. 2015. - XIV, 460 p. 221 illus., 7 illus. in color.online resource.

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

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

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

Linear Fractional Diffusion-Wave Equation for Scientists and Engineers
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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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