Estimation of parameters in fractional subdiffusion equations by the time integral characteristics method

This paper presents an extension to the time integral characteristics method for estimation of parameters in fractional subdiffusion equations containing Riemann–Liouville and Caputo fractional time derivatives. The explicit representations of the fractional diffusion coefficient and order of fractional differentiation via a Laplace transform of the concentration field are obtained. A technique of optimal Laplace parameter determination by minimization of relative errors bounds is described. The effectivity of the proposed approach is illustrated by numerical example.