Hermite-Hadamard type inequality for $\psi$-Riemann-Liouville fractional integrals via preinvex functions

Document Type : Research Paper


1 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India

2 Department of Mathematics, Statistics and Physics College of Arts and Sciences, Qatar University, P. O. Box 2713, Doha, Qatar


The main aim of the present paper is to establish a new form of Hermite-Hadamard inequalities using left and right-sided $\psi$-Riemann-Liouville fractional integrals for preinvex functions and present two basic results of $\psi$-Riemann-Liouville fractional integral identities including the first-order derivative of a preinvex function. We derive some fractional Hermite-Hadamard inequalities with the help of these results. Further, we pointed out some applications for special means.