Strict Hölder regularity for fractional order abstract degenerate differential equations

In this paper, we first characterize the behaviour of fractional resolvent families on the real interpolation spaces (X,D(A))θ,p,θ∈(0,1),p∈[1,∞]. Second, we establish strict Hölder regularity in space and time to an abstract degenerate fractional order differential equations. We also provide an application to illustrate our results.