  In this work, we investigate the IVP for a time-fractional fourth-order
equation with nonlinear source terms. More specifically, we consider the
time-fractional biharmonic with exponential nonlinearity and the
time-fractional Cahn-Hilliard equation. By using the Fourier transform concept,
the generalized formula for the mild solution as well as the smoothing effects
of resolvent operators are proved. For the IVP associated with the first one,
by using the Orlicz space with the function $ \Xi(z)=e^{|z|^p}-1$ and some
embeddings between it and the usual Lebesgue spaces, we prove that the solution
is a global-in-time solution or it shall blow up in a finite time if the
initial value is regular. In the case of singular initial data, the
local-in-time/global-in-time existence and uniqueness are derived. Also, the
regularity of the mild solution is investigated. For the IVP associated with
the second one, some modifications to the generalized formula are made to deal
with the nonlinear term. We also establish some important estimates for the
derivatives of resolvent operators, they are the basis for using the Picard
sequence to prove the local-in-time existence of the solution.
