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Modern Stochastics: Theory and Applications


On generalized stochastic fractional integrals and related inequalities
Volume 5, Issue 4 (2018), pp. 471–481
Pub. online: 24 September 2018      Type: Research Article      Open accessOpen Access
Received
29 May 2018
Revised
13 September 2018
Accepted
13 September 2018
Published
24 September 2018

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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Keywords
Hermite–Hadamard inequality stochastic fractional integrals convex stochastic process

MSC2010
26D15 26A51 60G99

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