On Pólya-Szegö integral inequalities using <i>k</i> -Hilfer fractional derivative

Abstract The main aim of this paper is to use the k -Hilfer fractional derivative to derive certain Pólya-Szegö fractional integral inequalities. Further fractional integral inequalities are obtained. The results presented here extend and generalize various existing inequalities associated with the Riemann-Liouville, Caputo, Saigo, and Hilfer fractional operators. The findings contribute to the growing theory of fractional calculus and offer potential tools for the analysis of fractional differential and integral equations.