In this paper, completeness problem for a class of fractional rational basis functions with incommensurable differentiation orders is studied. Using the Müntz-Sz`asz theory, it is established that the completeness problem for this class of the basis functions is equivalent to another completeness problem for a particular set of uncountably many basis functions. This equivalence allows one to draw fairly general conclusions on the nature of the completeness problem for fractional rational basis functions with incommensurable differentiation orders.