Inks?
Photographic prints have no inks. The colours are produced by dyes created during development in direct relation to exposed silver halide grains in three colour sensitive layers which are developed first and bleached out during final bleach/fix to leave just the relevant C, M & Y dyes.
These three colour layers form the image in the end: cyan, magenta and yellow adding together to produce the appearance of natural colour.
These layers fade at different rates over time at a rate that is determined by many factors, including initial manufacture, subsequent processing (type and state of the chemistry), and the display method and atmospheric conditions to which the print has been subject over its life. Add to this the variable but inconsistent rate of yellowing of the base material and you have the recipe for any number of outcomes, from a reddish print through to a light yellow-green (as in the left side of your example – plus a bit of staining) and anything in between.
Take a normal colour photo and using adjustment layers (Layer>Adjustment Layer>Channel Mixer….) make one adjustment layer for each of the Red, Green and Blue Channels. Increase the relevant channel’s output to imitate fading of its complimentary colour – i.e. increase red in the red channel to imitate cyan fading, green for magenta fading and blue for yellow fading – until you get the effect you’re after. Doing it this way will also lighten the picture appropriately to imitate overall fading.
Add a light yellowish brown transparent overlay to mimic the base yellowing and desaturate a bit, and you’ll get close.
In other words, just do the reverse of what you would do to restore a faded print’s colour.
So here’s an imitation of one that’s gone the greenish-yellow route (without any heavy yellow-brown staining):
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