Abstract An inverse problem for determining the order of the Caputo time-fractional derivative in a subdiffusion equation with an arbitrary positive self-adjoint operator A with discrete spectrum is considered. By the Fourier method it is proved that the value of ∥ A ⁢ u ⁢ ( t ) ∥ {\|Au(t)\|} , where u ⁢ ( t ) {u(t)} is the solution of the forward problem, at a fixed time instance recovers uniquely the order of derivative. A list of examples is discussed, including linear systems of fractional differential equations, differential models with involution, fractional Sturm–Liouville operators, and many others.

中文翻译：

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确定子扩散方程的 Caputo 时间分数阶导数的反问题

摘要 考虑了确定具有离散谱的任意正自伴随算子A的子扩散方程中Caputo时间分数阶导数的反问题。通过傅里叶方法证明了 ∥ A ⁢ u ⁢ ( t ) ∥ {\|Au(t)\|} 的值，其中 u ⁢ ( t ) {u(t)} 是前向问题的解，在固定时间实例唯一恢复导数的阶。讨论了一系列示例，包括分数阶微分方程的线性系统、带对合的微分模型、分数 Sturm-Liouville 算子等。