Fractional Hermite–Jensen–Mercer Integral Inequalities with respect to Another Function and Application

Abstract

In this paper, authors prove new variants of Hermite–Jensen–Mercer type inequalities using $\psi$ –Riemann–Liouville fractional integrals with respect to another function via convexity. We establish generalized identities involving $\psi$ –Riemann–Liouville fractional integral pertaining first and twice differentiable convex function $\lambda$ , and these will be used to derive novel estimates for some fractional Hermite–Jensen–Mercer type inequalities. Some known results are recaptured from our results as special cases. Finally, an application from our results using the modified Bessel function of the first kind is established as well.