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.
$$^{1}$$Corresponding Author: sajid_uos2000@yahoo.com
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.