Weighted Hardy–Littlewood–Sobolev-type inequality for ψ-Riemann–Liouville fractional integrals

Abstract

In this paper, we present a new extension for Hardy–Littlewood-type inequalities using the Riemann–Liouville fractional integral with respect to another function in the weighted Lebesgue space $L_{\mathit{\psi }}^p[a,b]$. These estimates are very important in the study of fractional differential equations with variational form and in the construction of fractional spaces of Sobolev type.