Propagation Speed of the Maximum of the Fundamental Solution to the Fractional Di usion-Wave Equation

摘要：

In this paper, the one-dimensional time-fractional diffusion-wave equation with the fractional derivative of order α; 1 < α < 2 is revisited. This equation interpolates between the diffusion and the wave equations that behave quite differently regarding their response to a localized disturbance: whereas the diffusion equation describes a process, where a disturbance spreads infinitely fast, the propagation speed of the disturbance is a constant for the wave equation. For the time-fractional diffusion-wave equation, the propagation speed of a disturbance is innite, but its fundamental solution possesses a maximum that disperses with a finite speed. In this paper, the fundamental solution of the Cauchy problem for the time-fractional diffusionwave equation, its maximum location, maximum value, and other important characteristics are investigated in detail. To illustrate analytical formulas, results of numerical calculations and plots are presented. Numerical algorithms and programs used to produce plots are discussed.

关键词： Time-fractional diffusion-wave equation Cauchy problem fundamental solution Wright function Mainardi function propagation speed maximum of fundamental solution numerical calculation of the Green function

作者: Yuri Luchko Francesco Mainardi Yuriy Povstenko

作者单位: Department of Mathematics,Beuth Technical University of Applied Sciences, Berlin, 13353 Germany Department of Physics,Bologna University and INFN, Bologna, 40126 Italy Institute of Mathematics and Computer Science, Jan Dlugosz University in Czestochowa, Czestochowa, 4

会议类型: 国际会议

会议名称: The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)

会议地点: 南京

会议语种:英文

页码: 1-8

在线出版日期: 2012-05-14（万方平台首次上网日期，不代表论文的发表时间）