On Hilbert-Pachpatte type inequalities within ψ-Hilfer fractional generalized derivatives

Abstract

In this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided ψ-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 ψ-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting ψ, a1, b1 and considering the limit of the parameters α and β.