Journal of Prime Research in Mathematics

Improvement of the Hardy inequality involving \(k\)-fractional calculus

Sajid Iqbal\(^1\)
Department of Mathematics, University of Sargodha (Sub-Campus Bhakkar), Bhakkar, Pakistan.
Muhammad Samraiz
Department of Mathematics, University of Sargodha, Sargodha, Pakistan.
\(^{1}\)Corresponding Author:


The major idea of this paper is to establish some new improvements of the Hardy inequality by using \(k\)-fractional integral of Riemann-type, Caputo \(k\)-fractional derivative, Hilfer \(k\)-fractional derivative and Riemann-Liouville \((k,r)\)-fractional integral. We discuss the \(\log\)-convexity of the related linear functionals. We also deduce some known results from our general results.


Convex function, kernel, fractional derivative, fractional integrals, means.