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We study the existence results of a fractional (<i>p</i>, <i>q</i>)-integrodifference equation with periodic fractional (<i>p</i>, <i>q</i>)-integral boundary condition by using Banach and Schauder’s fixed point theorems. Some properties of (<i>p</i>, <i>q</i>)-integral are also presented in this paper as a tool for our calculations.