Resolving operators of degenerate evolution equations with fractional derivative with respect to time

We consider resolving operators of a fractional linear differential equation in a Banach space with a degenerate operator under the derivative. Under the assumption of relative $p$-boundedness of a pair of operators in this equation, we find the form of resolving operators and study their properties. It is shown that solution trajectories of the equation fill up a subspace of a Banach space. We obtain necessary and sufficient conditions for relative $p$-boundedness of a pair of operators in terms of families of resolving operators for degenerate fractional differential equation. Abstract results are illustrated by examples of the Cauchy problem for degenerate finite-dimensional system of fractional differential equations and of initial boundary-value problem for a fractional equation with respect to the time containing polynomials of Laplace operators with respect to spatial variables.