Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

HOME ALL ARTICLES View

Commun. Korean Math. Soc. 2020; 35(1): 161-184

Online first article August 27, 2019      Printed January 31, 2020

https://doi.org/10.4134/CKMS.c180458

Copyright © The Korean Mathematical Society.

On some weighted Hardy-type inequalities involving extended Riemann-Liouville fractional calculus operators

Sajid Iqbal, Josip Pe\v cari\'c, Muhammad Samraiz, Hassan Tehmeena, \v Zivorad Tomovski

University of Sargodha (Sub-Campus Bhakkar); RUDN University; University of Sargodha; University of Sargodha (Mandi Bahauddin Campus); Institute of Mathematics

Abstract

In this article, we establish some new weighted Hardy-type inequalities involving some variants of extended Riemann-Liouville fractional derivative operators, using convex and increasing functions. As special cases of the main results, we obtain the results of \cite{spp, s1}. We also prove the boundedness of the $k$-fractional integral operator on $L_{p}[a,b]$.

Keywords: Hardy-type inequalities, Riemann-Liouville, fractional integral operator, convex and increasing function

MSC numbers: 26D15, 26D10, 26A33