In this paper, using a analytic univalent functions of the form f(z)=z+∑_{k=2}^{∞}a_{k}z^{k}, that is defined in the open unit disk U={z:|z|<1}. We define a class of functions by using Aouf et al. [3] operator D_{q,λ}ⁿ and Jackson q- derivative in the open unit disk U which for different values of its parameters many special new classes can be obtained from it. For this class of functions, we obtained some of its properties such as coefficient estimates, neighborhood of function and the modified Hadamard product of two functions in it and also for function which its coefficients are the sum of the squares of the coefficients of two functions. Key results demonstrate the influence of the Aouf et al. [3] operator on the univalence, growth theorems and distortion properties for this class of functions. Also we obtained analogue results of these results for each of the subclass obtained from this class.