A HIDDEN-MEMORY VARIABLE-ORDER TIME-FRACTIONAL OPTIMAL CONTROL MODEL: ANALYSIS AND APPROXIMATION

We prove the well-posedness and smoothing property of a fractional optimal control model with integral constraints governed by a hidden-memory variable-order Caputo time-fractional diffusion PDE, in which the adjoint equation leads to a different type of variable-order Riemann-Liouville time-fractional diffusion PDE. The L-1 discretization loses its monotonicity due to the impact of hidden memory, which was crucial in the error estimate of the L-1 discretization of constant-order fractional diffusion PDEs. We develop a novel splitting to prove an optimal-order error estimate of the discretization of the optimal control model without any artificial regularity assumption of the true solution. Numerical experiments are performed to substantiate the theoretical findings.