Improvement of the Hardy inequality involving k-fractional calculus

Authors

  • Sajid Iqbal Department of Mathematics, University of Sargodha (Sub-Campus Bhakkar), Bhakkar, Pakistan.
  • Muhammad Samraiz Department of Mathematics, University of Sargodha, Sargodha, Pakistan.

Keywords:

Convex function, kernel, Caputo-Fabrizio fractional derivative operator, fractional integrals, means

Abstract

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

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Published

2020-12-31

Issue

Vol. 16 No. 2 (2020): Journal of Prime Research in Mathematics

Section

Regular

How to Cite

Improvement of the Hardy inequality involving k-fractional calculus. (2020). Journal of Prime Research in Mathematics, 16(2), 89 – 108. https://jprm.sms.edu.pk/index.php/jprm/article/view/163