In this paper, the generalized fractional q-integral operator of the Kober type is applied to the basic analogue of the H-function.Results involving the basic hypergeometric functions J ν (x; q), Y ν (x; q), K ν (x; q), H ν (x; q), r+1 φ r (•), Mac-Robert's E-function and several elementary q-functions, have been deduced as particular cases of the main result.