Ostrowski-Type Fractional Integral Inequalities: A Survey

This paper presents an extensive review of some recent results on fractional Ostrowski-type inequalities associated with a variety of convexities and different kinds of fractional integrals. We have taken into account the classical convex functions, quasi-convex functions, $(\zeta ,m)$-convex functions, s-convex functions, $(s,r)$-convex functions, strongly convex functions, harmonically convex functions, h-convex functions, Godunova-Levin-convex functions, $MT$-convex functions, P-convex functions, m-convex functions, $(s,m)$-convex functions, exponentially s-convex functions, $(\beta ,m)$-convex functions, exponential-convex functions, $\overline{\zeta },\beta ,\gamma ,\delta$-convex functions, quasi-geometrically convex functions, $s-e$-convex functions and n-polynomial exponentially s-convex functions. Riemann–Liouville fractional integral, Katugampola fractional integral, k-Riemann–Liouville, Riemann–Liouville fractional integrals with respect to another function, Hadamard fractional integral, fractional integrals with exponential kernel and Atagana-Baleanu fractional integrals are included. Results for Ostrowski-Mercer-type inequalities, Ostrowski-type inequalities for preinvex functions, Ostrowski-type inequalities for Quantum-Calculus and Ostrowski-type inequalities of tensorial type are also presented.