Linear Fractional Diffusion-Wave Equation for Scientists and Engineers

• Main Author: Povstenko, Yuriy (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Subjects: Mathematics.; Partial differential equations.; Mathematical physics.; Physics.; Partial Differential Equations.; Mathematical Methods in Physics.; Mathematical Applications in the Physical Sciences.

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...

Table of 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.