Propagation speed of the maximum of the fundamental solution to the fractional diffusion–wave equation
In this paper, the one-dimensional time-fractional diffusion–wave equation with the fractional derivative of order α,1
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| Veröffentlicht in: | Computers & mathematics with applications (1987) 2013-09, Vol.66 (5), p.774-784 |
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| container_title | Computers & mathematics with applications (1987) |
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| creator | Luchko, Yuri Mainardi, Francesco Povstenko, Yuriy |
| description | In this paper, the one-dimensional time-fractional diffusion–wave equation with the fractional derivative of order α,1 |
| doi_str_mv | 10.1016/j.camwa.2013.01.005 |
| format | Article |
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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 infinite, 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 diffusion–wave 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. 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| ispartof | Computers & mathematics with applications (1987), 2013-09, Vol.66 (5), p.774-784 |
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| source | Elsevier ScienceDirect Journals Complete; EZB Electronic Journals Library |
| subjects | Cauchy problem Derivatives Fundamental solution Mainardi function Mittag-Leffler function Time-fractional diffusion–wave equation Wright function |
| title | Propagation speed of the maximum of the fundamental solution to the fractional diffusion–wave equation |
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