Journal of Prime Research in Mathematics
Vol. 17 (2021), Issue 1, pp. 48 – 58
ISSN: 1817-3462E (Online) 1818-5495 (Print)
ISSN: 1817-3462E (Online) 1818-5495 (Print)
Some Opial-type inequalities involving fractional integral operators
Sajid Iqbal\(^a\), Muhammad Samraiz\(^{b,*}\), Shahbaz Ahmad\(^c\), Shahzad Ahmad\(^a\)
\(^a\)Department of Mathematics, Ripha International University, Faisalabad Campus, Satyana Road, 38000 Faisalabad, Pakistan.
\(^b\)Department of Mathematics, University of Sargodha, Sargodha, Pakistan.
\(^c\)Department of Mathematics, University of Sargodha (Sub-Campus Bhakkar), Bhakkar, Pakistan.
Correspondence should be addressed to: Muhammad Samraiz at muhammad.samraiz@uos.edu.pk
Copyright © 2021 Sajid Iqbal, Muhammad Samraiz, Shahbaz Ahmad, Shahzad Ahmad. 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: Received: 6 April 2020; Accepted: 20 November 2020; Published Online: 11 June 2021.
Abstract
The core idea of this paper is to provide the Opial-type inequalities for Hadamard fractional integral operator and fractional integral of a function with respect to an increasing function \(g\). Moreover, related extreme cases and counter part of our main results are also given in the paper.
Keywords:
Inequalities, Kernel, fractional integrals.