Abstract
In this paper, we introduce stochastic g-fractional integrals of order $$ \alpha $$, containing stochastic fractional integrals (Hafiz in Stoch Anal Appl 22:507–523, 2004), stochastic integral (Shaked and Shanthikumar in Adv Appl Prob 20:427–446, 1988) and stochastic pseudo integrals (Agahi in Stat Probab Lett 124:41–48, 2017). We determine the upper and lower bounds of stochastic g-fractional integrals for convex stochastic processes, generalizing some previous results in Kotrys (Aequat Math 83:143–151, 2012), Agahi (Aequat Math 90:765–772, 2016; 2017) and Agahi and Babakhani (Aequat Math 90:1035–1043, 2016).
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