The q-fractional Euler top system with one control on a fractional Leibniz algebroid

We determine the fractional almost Poisson realizations for fractional Euler top system with one control. These realizations allow us to introduce a fractional Leibniz algebroid structure on R3 and also to define the q-fractional Euler top system with one control on a fractional Leibniz algebroid. Finally, the numerical integration of them are discussed.