A generalization of the ultra-hyperbolic time-fractional diffusion-wave equation introduced by the author in Dorrego [The Mittag–Leffler function and its application to the ultra-hyperbolic time-fractional diffusion-wave equation. Integral Transforms Spec. Funct. 2016;27(5):392–404] is presented and studied. The results obtained here extend the previous to the whole space ${\mathbb{R}}^n$. The problem is solved by applying the integral transforms method and the analytical solution is given by the Fox H-function. Some interesting particular cases are analysed.

中文翻译：

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广义时空分数阶超双曲微分方程的解析解

作者在 Dorrego [The Mittag-Leffler function and its application to the ultra-hyperbolic time-fractional diffusion-wave equation. 积分变换规范。功能。2016;27(5):392–404] 进行了介绍和研究。这里得到的结果将之前的扩展到整个空间${\mathbb{R}}^n$. 该问题通过应用积分变换方法解决，解析解由 Fox H函数给出。分析了一些有趣的特殊情况。