We investigate a local modification of a variable-order time-fractional wave equation, which models the vibrations of a viscoelastic bar along its longitudinal axis. Under suitable assumptions regarding the variable order at t=0, we prove that the original model is equivalent to a multiscale wave equation. Furthermore, we analyze the well-posedness of its weak solution. Numerical experiments are implemented to clarify the theoretical analysis.

中文翻译：

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变阶分数波动方程的局部修改和分析


我们研究了变阶时分波动方程的局部修改，该方程模拟了粘弹性棒沿其纵轴的振动。在关于 t=0 时的变量阶数的适当假设下，我们证明了原始模型等价于多尺度波动方程。此外，我们分析了其弱解的适定性。通过数值实验阐明了理论分析。