Some Unexplored Topics in The Reconstruction of Scalar Parameters of Subdiffusion
This work tackles incremental improvements in parameter estimation for subdiffusion models, relevant to researchers in applied mathematics and inverse problems.
The paper addresses the numerical reconstruction of scalar parameters in a fractional diffusion equation with memory effects, focusing on unresolved questions related to nonlocal observations in small time intervals, but does not report specific results or numbers.
In the paper, we discuss the reconstruction of scalar parameters in a linear diffusion equation with fractional in time differential operators and with additional nonlocal (convolution) terms, which incorporate memory effects in models. Although, under suitable assumptions on the data, inverse problems associated with recovery of these parameters are nowadays well understood, several important questions related with numerical reconstructions of these parameters via a nonlocal observation in a small time interval have not yet been analyzed. This paper aims to provide some answers.