Fractional Integral Inequalities Involving Convexity
DOI:
https://doi.org/10.5644/SJM.08.2.04Keywords:
Fractional integral, fractional radial derivative, Hardy fractional inequality, Poincar´e fractional inequality, Erd´elyi-Kober fractional integralsAbstract
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, $p\geq 1$, and exponential type.
2000 Mathematics Subject Classification. 26A33, 26D10, 26D15
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