A note on transfer-type function for nonlinear fractional order difference system

Using the polynomial description related to differentials of inputs and outputs in a difference field of meromorphic functions embedded in its quotient field a concept of a transfer-type function to nonlinear fractional order system with the Grünwald-Letnikov h-difference operator is given. Two different approaches to defining this function are presented. In the contrast to classical case, the transfer-type function is defined independently on initial conditions.