How should I interpret this function notation?

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I'm trying to implement an FDGD Algorithm from a paper and I'm a little stuck how to interpret a piece of function notation. See page 7, equations 2 and 3 in this document:

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In there we have $f_1^{1/2}(u)$ and $f_2^{1/2}(u)$. Am I supposed to interpret this as the half derivative? Or do they mean the functional square root?