Fractional order partial differential equations are very important mathematical models in describing lots of anomalous dynamic behaviors in multiple disciplines. This paper focuses upon the fractional order hyperbolic equation, which is influenced by different types of time-dependent oscillating coefficients on the principal operator part. We apply the essential techniques from harmonic analysis and probability analysis to explore the upper bound of loss of regularity. Furthermore, in order to demonstrate the optimality of the estimates, an appropriate counter-example with periodic coefficients is constructed to show the lower bound of loss of regularity by the application of instability arguments.

分数阶偏微分方程是描述多学科中大量异常动态行为的非常重要的数学模型。本文重点研究分数阶双曲方程，该方程受主算子部分不同类型的瞬态振荡系数的影响。我们应用调和分析和概率分析的基本技术来探索规律性损失的上限。此外，为了证明估计的最优性，构造了一个具有周期系数的适当反例，以显示通过应用不稳定性参数而失去规律性的下限。