  We explore the approximation of feedback control of integro-differential
equations containing a fractional Laplacian term.
  To obtain feedback control for the state variable of this nonlocal equation
we use the Hamilton--Jacobi--Bellman equation.
  It is well-known that this approach suffers from the curse of dimensionality,
and to mitigate this problem we couple semi-Lagrangian schemes for the
discretization of the dynamic programming principle with the use of Shepard
approximation. This coupling enables approximation of high dimensional
problems. Numerical convergence toward the solution of the continuous problem
is provided together with linear and nonlinear examples. The robustness of the
method with respect to disturbances of the system is illustrated by comparisons
with an open-loop control approach.
