Uniqueness and Existence for Inverse Problem of Determining an Order of Time-Fractional Derivative of Subdiffusion Equation

被引:12
作者
Ashurov, R. R. [1 ]
Fayziev, Yu E. [2 ]
机构
[1] Acad Sci Uzbek, Inst Math, Tashkent 100170, Uzbekistan
[2] Natl Univ Uzbekistan, Tashkent 700174, Uzbekistan
关键词
nonhomogeneous subdiffusion equation; Riemann-Liouville derivatives; inverse and initial-boundary value problem; determination of the fractional derivative's order; Fourier method; OPERATOR;
D O I
10.1134/S1995080221030069
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:508 / 516
页数:9
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