There’s a lot of debate over whether purple ink fades faster than other ink colours, although there seems to be anecdotal evidence that it does.
The colours that are known to fade the fastest are yellow, white, red, and green, but purple is also known for losing vibrancy quicker than black or blue inks. It also depends on the intensity and brightness of the colour - pastels and watercolour purples are likely to fade faster than an intense violet.
The most important factor in how a tattoo heals is aftercare. Keep fresh tattoos out of the sun (as prolonged exposure can cause healed tattoos to fade), make sure they don’t get too wet and use the best aftercare solutions, such as Hustle Butter Deluxe.