Rational inequalities for integral operators under convexity

Here we present integral inequalitites for convex and increasing functions applied to products of ratios of functions and other important mixtures. As applications we derive a wide range of fractional inequalities of Hardy type. They involve the left and right Riemann-Liouville fractional integrals and their generalizations, in particular the Hadamard fractional integrals. Also inequalities for Riemann-Liouville, Caputo, Canavati and their generalizations fractional derivatives. These application inequalities are of Lp type, p ± 1, exponential type and of other general forms. © Dynamic Publishers, Inc