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 muhammad.samraiz@uos.edu.pk

### 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.