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Journal of Applied Nonlinear Dynamics 2(1) (2012) 59--81 | DOI:10.5890/JAND.2012.09.005

George A. Anastassiou

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

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Abstract

Here we present Lp, p>1, vectorial integral inequalitites for products of multivariate convex and increasing functions applied to vectors of ratios of functions. As applications we derive a wide range of vectorial fractional inequalities of Hardy type. They involve the left and right Erdelyi-Kober fractional integrals and left and right mixed Riemann-Liouville fractional multiple integrals. Also we give vectorial inequalities for Riemann-Liouville, Caputo, Canavati radial fractional derivatives. Some inequalities are of exponential type.

References

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