On Grünwlad-Letinkov fractional operator with measurable order on continuous-discrete time scale

Considering experimental implementation control laws on digital tools that measurement cards are discharged every time unit one can see that time of simulations is partially continuous and partially discrete. This observation provides the motivation for defining the Grünvald-Letnikov fractional operator with measurable order defined on continuous-discrete time scale. Some properties of this operator are discussed. The simulation analysis of the proposed approach to the Grünwald-Letnikov operator with the measurement functional order is presented.