# On generalized stochastic fractional integrals and related inequalities

## TL;DR

This paper introduces generalized mean-square fractional integrals for stochastic processes and establishes a fractional Hermite-Hadamard inequality for Jensen-convex and strongly convex stochastic processes.

## Contribution

It defines new generalized stochastic fractional integrals and proves a novel fractional Hermite-Hadamard inequality for convex stochastic processes.

## Key findings

- Introduction of generalized mean-square fractional integrals
- Establishment of fractional Hermite-Hadamard inequality for convex processes
- Application to Jensen-convex and strongly convex stochastic processes

## 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.

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Source: https://tomesphere.com/paper/1902.01230