The article presents a solution to a boundary value problem for a wave equation containing a fractional derivative with respect to a spatial variable. This model is used to describe oscillation processes in a viscoelastic medium, in particular changes in the deformation-strength characteristics of polymer concrete (dian and dichloroanhydride-1,1-dichloro-2,2-diethylene) under the influence of the gravity force. Based on the obtained solution to the boundary value problem, the article presents four numerical examples corresponding to homogeneous boundary conditions and various initial conditions. The graphs of the found solutions were constructed and the calculation accuracy in the considered examples was estimated.

中文翻译：

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分数阶导数的波动方程对聚合物混凝土强度特性的建模

本文提出了一个波动方程的边值问题的解决方案，该波动方程包含相对于空间变量的分数导数。该模型用于描述粘弹性介质中的振动过程，特别是在重力作用下聚合物混凝土（双氯二酐和1,1-二氯-2,2-二乙烯）的变形强度特性的变化。基于所获得的边值问题的解决方案，本文给出了对应于齐次边界条件和各种初始条件的四个数值示例。构建找到的解的图，并评估所考虑示例的计算精度。