Uniqueness of determining the variable fractional order in variable-order time-fractional diffusion equations. (24th October 2019)

• Record Type: Journal Article
• Authors: Zheng, Xiangcheng; Cheng, Jin; Wang, Hong
• Is Part Of: Inverse problems. Volume 35:Number 12(2019)
• Publication Date: 2019-10-24
• Subjects: determination of variable order -- variable-order time-fractional diffusion equation -- inverse problem -- uniqueness; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab3aa3
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Variable-order time-fractional diffusion equations provide very competitive modeling capabilities of challenging phenomena including anomalously subdiffusive transport of solutes in heterogeneous porous media and memory effect as constant-order time-fractional diffusion equations do, while eliminating the nonphysical singularity of the solutions near the initial time of the latter. Moreover, variable-order time-fractional diffusion equations themselves occur in many applications. We study the initial-boundary value problem of variable-order time-fractional diffusion equations and prove the uniqueness of determining the variable order in the initial-boundary value problem, from the observations of its solution on a sufficiently small open spatial interval over a sufficiently small time interval.