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  1. 1 Anastassiou G.

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Vectorial fractional integral inequalities with convexity

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Anastassiou G.
Open Physics
|
2013
|
vol. 11
|
issue 10
1194-1211
EN
Here we present vectorial general integral inequalities involving products of multivariate convex and increasing functions applied to vectors of functions. As specific applications we derive a wide range of vectorial 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 vectorial fractional inequalities 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.
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