On some weighted Hardy-type inequalities involving extended Riemann-Liouville fractional calculus operators
Commun. Korean Math. Soc. 2020 Vol. 35, No. 1, 161-184
Published online January 31, 2020
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
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