Fractional Integral Inequalities Involving Convexity - Anastassiou, George A. (Sarajevo Journal of Mathematics, 2024)
Here we present general integral inequalitites involving convex and increasing functions applied to products of functions. As specific applications we derive a wide range of fractional inequalities of Hardy type. These involve the left and right: Erdélyi-Kober fractional integrals, mixed Riemann-Liouville fractional multiple integrals. Next we produce multivariate Poincaré type fractional inequalitites involving left fractional radial derivatives of Canavati type, Riemann-Liouville and Caputo types. The exposed inequalities are of $L_{p}$ type, $p≥ 1$, and exponential type. 2000 Mathematics Subject Classification. 26A33, 26D10, 26D15