In this paper, we consider a non-homogeneous time–space-fractional telegraph equation in n-dimensions, which is obtained from the standard telegraph equation by replacing the first- and second-order time derivatives by Caputo fractional derivatives of corresponding fractional orders, and the Laplacian operator by a fractional Sturm–Liouville operator defined in terms of right and left fractional Riemann–Liouville derivatives. Using the method of separation of variables, we derive series representations of the solution in terms of Wright functions, for the homogeneous and non-homogeneous cases. The convergence of the series solutions is studied by using well known properties of the Wright function. We show also that our series can be written using the bivariate Mittag-Leffler function. In the end of the paper some illustrative examples are presented.

在本文中，我们考虑一个非齐次的时空分数电报方程在n-dimensions，从标准电报方程中获得，通过用相应分数阶的 Caputo 分数阶导数代替一阶和二阶时间导数，并用根据左右分数定义的分数 Sturm-Liouville 算子代替拉普拉斯算子黎曼-刘维尔导数。对于齐次和非齐次情况，我们使用分离变量的方法根据 Wright 函数推导出解的级数表示。级数解的收敛性是通过使用 Wright 函数的众所周知的特性来研究的。我们还展示了我们的系列可以使用二元 Mittag-Leffler 函数编写。在论文的最后，给出了一些说明性的例子。