There is nothing in the rules or the prone condition that says a grappling creature (or any creature, really) can do anything to help them up. This is likely due to the fact that the cases in which you would want to help a prone opponent to stand up were not common enough to justify writing explicit rules for.
However, this is more generally covered in the Improvising an Action section of the Combat rules (PHB, p.193):
Your character can do things not covered by the actions in this chapter [ ... ] The only limits to the actions you can attempt are your imagination and your character's ability scores.
When you describe an action not detailed elsewhere in the rules, the DM tells you whether that action is possible and what kind of roll you need to make, if any, to determine success or failure.
So the answer really boils down to "yes, but you'll need to ask your DM to make a ruling."
Possible Approaches to a Ruling
From a design perspective, "forcing a prone creature out of prone against its will" seems to parallel the Shove attack, in which you "force a creature to be prone against its will". Therefore, allowing this as a Special Melee Attack using a contest rather than a full action would be a reasonable (which would allow you to expend the rest of any Extra Attacks you may have).
That said, I don't see any particular balance issues arising from expending an action to force a prone creature to stand up. The cost there seems sufficient, and is at least simpler than the alternative (which may be preferred for something that will not come up often.)