Yes. It's called learning, and you can use just about any app to do it. Note taking apps, lecture/course apps, flash card apps, you name it.

But an app that arbitrarily claims to "improve your brain" with little addicting games? That's the opposite thing. Good luck

Sudoku is one that's been studied and shown, so far, to help with some cognitive issues.

Role of prefrontal cortex during Sudoku task: fNIRS study

asking this is like asking whether there is a single gym routine that works out all muscles of the body.

there isn't. because what strains your pecs is different from what strains your glutes. that's why we have different routines for different muscle groups.

the brain isn't a just a simple little box. it has multiple functions which are triggered by vastly different stimuli. relying on "brain training" apps would be akin to only doing bicep curls every day--sure, your guns will be super but the rest of your body will still remain flabby and weak forever.

From what I have read there isn't any legitimate brain training apps for the average person. I know there are apps out there to help with specific disorders and things like that having some positive results, but everything I have seen on brain training shows little benefit from it, and it is really just a way to make yourself feel like you are doing something from what I can tell.

That being said, as someone with a bad memory, keeping a detailed journal and writing important or interesting things down when they happen help me remember things much better. If you can say what you want to remember out loud that is even better because it is another way to solidify what you are trying to remember.

A trick my counselor taught me is to Journal before bed, read what you wrote when you are finished, and then go to sleep. This is supposed to help with long term memory of what you wrote down, and I have seen improvement doing this with my long term memory.

Factorio will challenge all of your mental capabilities

Portal & Portal 2

And if you're really feeling masochistic, Portal Reloaded

Your brain gets good at what it does. There’s a bit of skill transfer here and there but overall, training your brain on brain training games trains your brain to play brain training games. Practice what you want to get good at

I see Brilliant.org advertised often in educational YouTube, so that might be a good start. Those channels often have promo codes too

Learn a language! There’s been a lot of research in language learning being greatly beneficial for your brain. It’s also an incredibly useful skill to be able to communicate with more people

I would say:

• Reading books
• Playing chess

Both can be done on a phone I suppose.

Lichess

Here's what I do on my phone most of the time nowadays:

• Practice sudoku @ sudoku.coach
• Practice chess @ Lichess
• Practice Japanese @ renshuu.org

I almost got rid of all of my doomscrolling with actual brain activity. It feels great, and having different topics to choose from helps break the monotony.

I'd say Anki

I like sudoku and math problems

Books, physical puzzles or puzzle games, deep diving into a topic/hobby. Just do STUFF. Don't overthink it.

I don't know if Brain Age has any legitimate scientific value but it sure as heck is fun. Don't buy the switch version though, that one sucks.

Tetris. IIRC there are some very positive studies backing it. There is even something called the "Tetris Effect" (not the game).