In this paper, two weighted parameterized fractal identities are first proposed, wherein the mappings involved are second-order local fractional differentiable. Based upon these equalities, a series of the weighted parameterized inequalities, which are related to the fractal convex mappings, are then deduced. Moreover, making use of boundedness and [Formula: see text]-Lipschitzian mappings, some error estimates are attained as well. Finally, certain fractal outcomes in accordance to random variable and the weighted formula, respectively, are presented as applications.