On the well-posedness of an inverse problem for a degenerate evolutionary equation with the Dzhrbashyan–Nersesyan fractional derivative

In this paper, we find necessary and sufficient conditions for the well-posedness of linear inverse coefficient problems for degenerate evolutionary equations with the Dzhrbashyan–Nersesyan fractional derivative in Banach spaces. We examine an inverse problem with a constant unknown coefficient under the generalized Showalter–Sidorov conditions and the condition of $p$-boundedness of a pair of operators in it. The general result is applied to the inverse problem for the system of dynamics of a viscoelastic Kelvin–Voigt fluid with the Dzhrbashyan–Nersesyan fractional derivative in time.