Optimality condition of the Pontryagin maximum principle type in the control problem of fractional series linear difference equations

The optimal control problem of fractional order linear two-dimensional difference equations systems is considered. It is assumed that the control function is included in the boundary condition, and the functional is linear. A necessary and sufficient optimality condition is proved in the discrete maximum principal form. A sufficient optimality condition is proved in the nonlinear but convex cost functional case.