Linear Fractional Diffusion-Wave Equation for Scientists and Engineers

  • Yuriy Povstenko

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Yuriy Povstenko
    Pages 1-4
  3. Yuriy Povstenko
    Pages 5-34
  4. Yuriy Povstenko
    Pages 35-40
  5. Yuriy Povstenko
    Pages 253-276
  6. Back Matter
    Pages 433-460

About this book

Introduction

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.

Keywords

Caputo derivative Fractional calculus Integral transforms Mittag-Leffler function diffusion-wave equation

Authors and affiliations

  • Yuriy Povstenko
    • 1
  1. 1.Jan Długosz University in CzęstochowaCzęstochowaPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-17954-4
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-17953-7
  • Online ISBN 978-3-319-17954-4
  • About this book