  This paper is concerned with the inverse problem of retrieving the initial
value of a time-fractional fourth order parabolic equation from source and
final time observation. The considered problem is an {\it ill-posed problem.}
We obtain regularized approximations for the sought initial value by employing
the quasi-boundary value method, its modified version and by Fourier truncation
method(FTM). We provide both the apriori and aposteriori parameter choice
strategies and derive the error estimates for all these methods under some {\it
source conditions} involving some Sobolev smoothness. As an important
implication of the obtained rates, we observe that for both the apriori and
aposteriori cases, the rates obtained by all these three methods are same for
some source sets. Moreover, we observe that in both the apriori and aposteriori
cases, the FTM is free from the so-called {\it saturation effect}, whereas both
the quasi-boundary value method and its generalizations possesses the
saturation effect for both the cases. Further, we observe that the rates
obtained by the FTM is always order optimal for all the considered source sets.
