Linear Fractional Diffusion-Wave Equation for Scientists and Engineers

Linear Fractional Diffusion-Wave Equation for Scientists and Engineers

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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 a€œlong-taila€ power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fouriera€™s, Ficka€™s and Darcya€™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.Special functions appearing in the particular cases of the solutions were computed according to routines descibed in [194]. The Mittag-Leffler functions were calculated by FORTRAN programs that implement the algorithms proposed in [52]anbsp;...

Title:Linear Fractional Diffusion-Wave Equation for Scientists and Engineers
Author: Yuriy Povstenko
Publisher:Birkhäuser - 2015-07-03

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