On a generalized boundary value problem for a feedback control system with infinite delay

We consider a non-local boundary value problem for feedback control system described by semilinear functional-differential inclusion of fractional order with infinite delay in separable Banach space. The general principle existence solutions to the terms difference from zero topological degree corresponding vector field is given. prove concrete example (Theorem 6) implementation this principle. an optimal solution posed proved, which minimizes given lower semicontinuous quality functional.