Abstract In paper the nonlinear inverse problem of finding a control parameter in a space-time fractional diffusion equation with varying degrees of heterogeneity is investigated. An iterative method for finding an unknown control parameter is proposed. Under the maximal regularity condition respecting input data on the Bessel potential scale, the existence and uniqueness of a solution of such inverse problem are shown. Results are illustrated by examples. An example of numerical simulation of an iterative algorithm is given.

中文翻译：

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时空分数阶扩散方程控制扩散参数确定的非线性反问题

摘要 本文研究了在具有不同程度非均质性的时空分数扩散方程中寻找控制参数的非线性逆问题。提出了一种寻找未知控制参数的迭代方法。在贝塞尔势标度输入数据的最大正则性条件下，显示了此类逆问题解的存在性和唯一性。结果通过实例说明。给出了迭代算法的数值模拟示例。