Reconstruction of a fractional evolution equation with a source

Abstract

We are concerned with the inverse problem of reconstructing a fractional evolution equation with a source. To this end we use observations of the solution on the boundary to reconstruct the principal part of the operator and the fractional order of the time derivative, while an overdetermination at a time T is used to recover the source by a non iterative method. Numerical examples explain how to compute the fractional order and the source using finite data.