DIFFUSIVITY IDENTIFICATION IN A NONLINEAR TIME-FRACTIONAL DIFFUSION EQUATION

This paper deals with the estimates of the convergence rates for various problems associated with diffusivity identification in a time-fractional nonlinear diffusion equation. We find the convergence rate of the corresponding Erdelyi-Kober type operator as the anomalous parameter approaches the classical limit. Further, we use this result in proving an estimate of the difference between the identified diffusivity and its approximate value which was derived by the use of the previously developed framework. The exact formula for the diffusivity is computationally expensive thus having an accurate and easily calculable approximation is very relevant. In the last part of the paper we take up the problem of regularization strategy for solving the inverse problem. Calculation of the diffusivity requires a computation of the derivative which is a unstable operation and can amplify the measurement noise. We discuss how this ill-possedness can be mollified and prove some corresponding estimates on the convergence rates of the regularization.