Singularities of generic linkage via Frobenius powers

Let $I$ be an equidimensional ideal of a ring polynomial $R$ over $\mathbb{C}$ and let $J$ be its generic linkage. We prove that there is a uniform bound of the difference between the F-pure thresholds of $I_p$ and $J_p$ via the generalized Frobenius powers of ideals. This provides evidence that the F-pure threshold of an equidimensional ideal $I$ is less than that of its generic linkage. As a corollary we recover a result on log canonical thresholds of generic linkage by Niu.