Fourier truncation method for the non-homogeneous time fractional backward heat conduction problem

This paper is devoted to the problem of determining the initial data for the backward non-homogeneous time fractional heat conduction problem by the Fourier truncation method. The exact solution for the forward and backward fractional heat problems is expressed in terms of eigen function expansion and Mittag-Leffler function. Due to the instability of determining initial data, a regularized truncated solution is considered. Further, the stability estimate for the exact solution and the convergence estimates for the regularized solution using an a-priori choice rule and an a-posteriori choice rule are derived.