Abstract
In this paper, we investigate the Hölder continuity and the estimate for the box dimension of the Weyl fractional integral of some continuous function [Formula: see text], denoted by [Formula: see text]. We obtain that if [Formula: see text] is [Formula: see text]-order Hölder continuous, then [Formula: see text] is [Formula: see text]-order Hölder continuous. Moreover, if [Formula: see text] belongs to [Formula: see text], then [Formula: see text] is [Formula: see text]-order Hölder continuous with [Formula: see text].
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