Representation of a solution for a system of linear inhomogeneous two-dimensional difference equations of fractional order

One linear inhomogeneous two-parameter discrete fractional system is considered, and the boundary condition is a solution of an analogue of the Cauchy problem for a linear ordinary difference equation. Equation coefficients are given by discrete matrix functions. By introducing an analogue of the Riemann matrix, representations of solutions of the considered boundary value problem are obtained. Note that the result obtained plays an essential role in the linear case for establishing a necessary and sufficient optimality condition in the form of the Pontryagin maximum principle, and also in the general case for studying special control in discrete optimal control problems for systems of 2D fractional orders.