Abstract In this paper, we consider a final value problem for the following time-fractional diffusion system: D t α u + 𝒜 u = F (u, v), D t α v + ℬ v = G (u, v), \{aligned Dₓ^{u+Au&% =F (u, v), \\ Dₓ^v+Bv&=G (u, v), aligned. where 𝒜 A and ℬ B are symmetric uniformly elliptic operators defined on a bounded domain Ω in ℝ d R^{d} with sufficiently smooth boundary and D t α Dₓ^{} refers to the Caputo fractional derivative of order 1 α 2 1<<2. Under suitable assumptions, we establish the existence and uniqueness of the solution to the problem and prove that the problem is ill-posed in the sense of Hadamard. A filter regularization method is proposed to approximate the solution and estimate the error between the regularized solution and the exact solution.
Nguyen et al. (Thu,) studied this question.