Frobenius nonclassical components of curves with separated variables

We establish a relation between minimal value set polynomials defined over FqFq and certain q  -Frobenius nonclassical curves. The connection leads to a characterization of the curves of type g(y)=f(x)g(y)=f(x), whose irreducible components are q-Frobenius nonclassical. An immediate consequence will be the realization of rich sources of new q-Frobenius nonclassical curves.