Journal of Prime Research in Mathematics
Vol. 16 (2020), Issue 2, pp. 89 – 108
ISSN: 1817-3462E (Online) 1818-5495 (Print)
ISSN: 1817-3462E (Online) 1818-5495 (Print)
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: sajid_uos2000@yahoo.com
Department of Mathematics, University of Sargodha (Sub-Campus Bhakkar), Bhakkar, Pakistan.
Muhammad Samraiz
Department of Mathematics, University of Sargodha, Sargodha, Pakistan.
\(^{1}\)Corresponding Author: sajid_uos2000@yahoo.com
Copyright © 2020 Sajid Iqbal, Muhammad Samraiz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: December, 2020
Abstract
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.
Keywords:
Convex function, kernel, fractional derivative, fractional integrals, means.