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 $ \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 $.

Keywords

• hilbert-pachpatte type inequality
• $ \psi $-hilfer fractional derivative
• riemann-liouville derivative
• homogeneous kernel
• fractional derivative