On nonlocal backward problems for fractional stochastic diffusion equations

This paper is devoted to solving a nonlocal backward problem for fractional stochastic diffusion equations. Based on the eigenfunction expansion of the solution, the nonlocal backward problem for searching the previous values is reduced to an integral equation. We obtain the boundedness, strong continuity and compactness of the new operators generated by the nonlocally terminal value term, and then we proceed to obtain the existence of mild solutions for the nonlocal backward problem. (C) 2019 Elsevier Ltd. All rights reserved.