Journal of Prime Research in Mathematics

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


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.


Inequalities, Kernel, fractional integrals.