Fading usually involves two problems:
- Each channel fades in different amounts
- Each channel fades differing amount is its highlight compared to its shadows.
A third factor is that in severe cases, one color may have faded so severely that there is a large loss of detail in that color while other colors have faded far less.
#1, above, can be dealt with adequately with global adjustments, but #2 requires using an adjustment method that not only allows for adjusting each color separately but also adjusting the shadow, midtone, and highlight components of each color independently. I've found that Photoshop's Curves adjustments are the best for this, sometimes in combination with its HSL adjustments to manage saturation on a color by color basis as well.
The the third factor raises its ugly head, nothing can be done to get anything in the way of an accurate correction. It is sometimes possible to get an acceptable result and sometimes conversion to B&W is a better choice. I have some chromes (E-2 process Ektachrome or possibly other brand) that are so faded in some colors that they are almost monochrome, hence B&W conversion is the most pleasing.