中文摘要：

通过光钳实验获取粒子的均方位移并据此建模是微观流变学中计算介质的局部响应函数的常用方法之一。本文考虑单脉冲噪声驱动的分数阶调和振子的均方位移。利用Laplace变换及双Laplace变换技巧,本文得到了振子的均值、方差及相关函数,进而求得均方位移。然后本文基于均方位移的渐近行为研究了振子的短时及长时扩散行为。研究表明,振子的短时扩散是弹道的而在长时则幂律地趋近于均衡值。

英文摘要：

Mean square displacements have oeen extensively - of viscoelastic medium in laser tweezer experiments. In this paper, by using the Laplace and double La- place transform techniques, we obtain the exact expression of position of a fractional harmonic oscillator driven by an impulsive noise. Then, the mean, variance, correlation function and mean square displacement of the oscillator are given in terms of the time-lag. Furthermore, diffusive behavior of the oscillator for short and long time-lag is investigated by considering the asymptotic behavior of the mean square displacement. It is shown that the oscillator undergoes a ballistic motion for short time-lag and a power- law decay to an equilibrium position for long time-lag.