Abstract This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoelliptic operators, with homogeneous multi-point time-nonlocal conditions. Several examples of the settings where our nonlocal problems are applicable are given. The results for the discrete spectrum are also applied to treat the case of general homogeneous hypoelliptic left-invariant differential operators on general graded Lie groups, by using the representation theory of the group. For all these problems, we show the existence, uniqueness, and the explicit representation formulae for the solutions.

中文翻译：

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一个多项分数阶扩散波动方程的非局部问题

摘要 本文讨论了具有离散谱的一般算子以及具有齐次多点时间非局部条件的正亚椭圆算子的时间分数扩散波方程的多项推广。给出了几个适用于我们的非局部问题的设置示例。利用群的表示理论，离散谱的结果也被用于处理一般分级李群上的一般齐次亚椭圆左不变微分算子的情况。对于所有这些问题，我们展示了解的存在性、唯一性和显式表示公式。