shift model curve over experimental curve in the y- and x- axes

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Hello,
I would like to shift model curve over experimental curve in the y- and x- axes (by using the least squares method, I presume). Both curves have the same step on x-axis (dx). For the y-axis I presume this can also be done with resampling.
Having this in mind, is it possible to shift the model curve over experimental curve in the y- and x- axes so that I get the best match ? The curves are of different lengths (on both x- and y-axes).
The model curve cannot be written as a y=f(x) formula for it is the result of a weird double integral equation.
Do you happen to know an elegant solution to this ?

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