Ashurov Ravshan, Umarov Sabir
Institute of Mathematics, Uzbekistan Academy of Science Tashkent, 81 Mirzo Ulugbek str., 100170 Uzbekistan.
Department of Mathematics, University of New Haven, 300 Boston Post Road, West Haven, CT 06516 USA.
Fract Calc Appl Anal. 2020;23(6):1647-1662. doi: 10.1515/fca-2020-0081. Epub 2020 Dec 31.
The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator. We prove that the additional information about the solution at a fixed time instant at a monitoring location, as "the observation data", identifies uniquely the order of the fractional derivative.
在应用分数阶建模中确定方程的正确阶数起着重要作用。在本文中，我们考虑一个反问题，即确定具有任意二阶椭圆型微分算子的次扩散方程中时间分数阶导数的阶数。我们证明，在监测位置固定时刻关于解的附加信息，即“观测数据”，能唯一确定分数阶导数的阶数。
