In this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided $\psi$-Hilfer fractional derivatives with the general kernel. Our results are a generalization of the inequalities of Pečarić and Vuković ^[1]. Furthermore, using the specific cases of the $\psi$-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting $\psi$, $a_1$, $b_1$ and considering the limit of the parameters $\alpha$ and $\beta$.