Abstract

An inverse problem for determining the order of time-fractional derivative in a nonhomogeneous subdiffusion equation with an arbitrary elliptic differential operator with constant coefficients in \(N\)-dimensional torus is considered. Using the classical Fourier method it is proved, that the value of the solution at a fixed time instant as the observation data recovers uniquely the order of fractional derivative. Generalization to an arbitrary \(N\)-dimensional domain and to elliptic operators with variable coefficients is considered.

中文翻译：

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确定二次扩散方程的时间分数阶导数阶的反问题的唯一性和存在性

摘要

考虑了用于确定具有在（（n））维环面中具有恒定系数的任意椭圆微分算子的非齐次扩散方程中时间分数阶导数阶数的反问题。使用经典的傅里叶方法，证明了在固定时刻作为观测数据的解的值唯一地恢复了分数导数的阶数。考虑推广到任意\（N \）维域和具有可变系数的椭圆算子。