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On the Fractional Wave Equation
Mathematics ( IF 2.4 ) Pub Date : 2020-05-31 , DOI: 10.3390/math8060874
Francesco Iafrate , Enzo Orsingher

In this paper we study the time-fractional wave equation of order 1 < ν < 2 and give a probabilistic interpretation of its solution. In the case 0 < ν < 1 , d = 1 , the solution can be interpreted as a time-changed Brownian motion, while for 1 < ν < 2 it coincides with the density of a symmetric stable process of order 2 / ν . We give here an interpretation of the fractional wave equation for d > 1 in terms of laws of stable d dimensional processes. We give a hint at the case of a fractional wave equation for ν > 2 and also at space-time fractional wave equations.

中文翻译:

关于分数波方程

在本文中,我们研究阶次的时分波方程 1个 < ν < 2 并给出其解决方案的概率解释。在这种情况下 0 < ν < 1个 d = 1个 ,该解可以解释为时变布朗运动,而对于 1个 < ν < 2 它与阶对称稳定过程的密度一致 2 / ν 。我们在这里给出分数波方程的解释 d > 1个 就稳定定律而言 d - 尺寸过程。我们给出了分数波方程的情况的提示 ν > 2 以及时空分数波方程。
更新日期:2020-05-31
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