Abstract We analyze the inverse boundary value-problem to determine the fractional order ν of nonautonomous semilinear subdiffusion equations with memory terms from observations of their solutions during small time. We obtain an explicit formula reconstructing the order. Based on the Tikhonov regularization scheme and the quasi-optimality criterion, we construct the computational algorithm to find the order ν from noisy discrete measurements. We present several numerical tests illustrating the algorithm in action.

中文翻译：

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确定半线性子扩散方程中的分数阶

摘要 我们分析了反边界值问题，以确定具有记忆项的非自治半线性子扩散方程的分数阶 ν，从它们的解的观测值在短时间内。我们获得了一个显式的公式来重构顺序。基于 Tikhonov 正则化方案和准最优准则，我们构建了计算算法以从有噪声的离散测量中找到阶 ν。我们提出了几个数值测试来说明算法的实际应用。