A spectral Petrov-Galerkin method is developed to solve an optimal control problem governed by a two-sided space-fractional diffusion-reaction equation with additive fractional noise. In order to compensate weak singularities of the solution near boundaries, regularity of both the fractional noise and the optimal control problem is analyzed in weighted Sobolev space. The spectral Petrov-Garlerkin method is presented by employing truncated spectral expansion of the fractional Brownian motion (fBm) type noise, and error estimates are given based on the obtained regularity of the optimal control problem. Numerical experiments are carried out to verify the theoretical findings. 

Professor Wanrong Cao received her Ph.D. in Mathematics from Harbin Institute of Technology in 2004. Then she joined the faculty of the School of Mathematics at Southeast University. She was promoted to a Professor in 2017. Her research is concerned with numerical methods of differential equations, especially the convergence rate and stability of numerical schemes for stochastic differential equations with or without time delay, construction of efficient numerical methods and error estimates for fractional differential equations.