We propose a numerical reconstruction method for solving a time-fractional backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurements of transient temperature at a fixed final time. The standard Tikhonov regularization technique using the norm of reproducing the kernel Hilbert space as the penalty term is adopted to provide a stable solution when the measurement data contains noise. Numerical results indicate that the proposed method is efficient.
"A Discretized Tikhonov Regularization Method for a Fractional Backward Heat Conduction Problem." Abstr. Appl. Anal. 2014 (SI64) 1 - 12, 2014. https://doi.org/10.1155/2014/964373