  This paper is concerned with recovering the solution of a final value problem
associated with a parabolic equation involving a non linear source and a
non-local term, which to the best of our knowledge has not been studied
earlier. It is shown that the considered problem is ill-posed, and thus, some
regularization method has to be employed in order to obtain stable
approximations. In this regard, we obtain regularized approximations by solving
some non linear integral equations which is derived by considering a truncated
version of the Fourier expansion of the sought solution. Under different Gevrey
smoothness assumptions on the exact solution, we provide parameter choice
strategies and obtain the error estimates. A key tool in deriving such
estimates is a version of Gr{\"o}nwalls' inequality for iterated integrals,
which perhaps, is proposed and analysed for the first time.
