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

Format:

Book

Author/Creator:

Povstenko, Yuriy, Author.

Language:

English

Subjects (All):

Differential equations.

Mathematical physics.

Differential Equations.

Mathematical Methods in Physics.

Mathematical Physics.

Local Subjects:

Differential Equations.

Mathematical Methods in Physics.

Mathematical Physics.

Physical Description:

1 online resource (470 p.)

Edition:

1st ed. 2015.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

3-319-17954-3