This paper presents the exact solutions of the homogeneous and the non-homogeneous fractional delay oscillation equations with order $\alpha \in (1,2)$. For non-homogeneous fractional delay oscillation equation, the Laplace transform is taken up as solving method in that it efficiently avoids some restrictions to the non-homogeneous term. Thereafter, we investigate the Hyers–Ulam stability of the fractional delay oscillation equation.

中文翻译：

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具有纯延迟的分数阶振动方程的精确解和Hyers-Ulam稳定性

本文给出了齐次和非齐次分数阶时滞振动方程的精确解。 $\alpha \in （\mathrm{1个}，2）$。对于非齐次分数阶延迟振动方程，拉普拉斯变换作为求解方法，因为它有效地避免了对非齐次项的某些限制。此后，我们研究分数延迟振荡方程的Hyers-Ulam稳定性。