My best guess here would be failing backlight LEDs on your screen. If the backlight driving circuits were going out it would affect all of the backlights uniformly (or at least a full half of the screen, depending) so I'm betting on some individual LEDs going out which can have a cascading effect on others.
To the best of my knowledge it's not common practice to attempt to replace the backlight LEDs on a laptop display, so I'd say you're going to have to replace the screen to fix this issue.
Fortunately, LCD replacement on your laptop is actually fairly easy, and iFixit already has a guide just waiting for you.
[guide|123048|Dell Latitude E7440 Screen Replacement - iFixit Repair Guide]
In terms of finding a replacement screen, you can of course search based on the model number of your laptop, but since very few laptop manufacturers actually make their own LCDs you can also try finding a replacement using the LCD's model number instead. Just follow the instructions up to Step 4 so you can get to the rear side of the LCD, where you will find a manufacturer's label with their name and the model number of the LCD. You can also use that information to find a replacement part. In addition, a general search may turn up the make and model number of other laptops that use that same LCD, and if that happens you can use that model number to also search for a screen.
That should give you several options for finding a replacement screen, hopefully that will fix the issue you're seeing.