On generalized stochastic fractional integrals and related inequalities

Abstract

The generalized mean-square fractional integrals ${\mathcal{J}}_{\rho ,\lambda ,u+;\omega }^{\sigma }$ and ${\mathcal{J}}_{\rho ,\lambda ,v-;\omega }^{\sigma }$ of the stochastic process $X$ are introduced. Then, for Jensen-convex and strongly convex stochastic proceses, the generalized fractional Hermite--Hadamard inequality is establish via generalized stochastic fractional integrals.

Published at https://doi.org/10.15559/18-VMSTA117 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/)