Parallel realization of the variable-, fractional-order difference equation

In the paper a block-matrix form of the variable-, fractional-order linear time-invariant difference equation is investigated. It is proved that similar to the state-space representation but with linearly increasing matrix-vector dimensions is useful in the difference equation solution. The block diagram of the system is described by the Jordan-like canonical form. It uses the variable-, fractional-order integrators and proportional blocks. The proposed approach simplifies numerical calculations of solutions due to a possibility of parallel computations. Analysis is supported by the numerical example.