Can I recover my deleted world?

Honestly, no.

This applies for all games on all iOS devices due to having no access to raw files and the way files are stored.

So, why?
iOS files are stored in a file architecture completely different to PC. The way files are stored is similar to how NBT tags work in Minecraft (yet are still completely different).
When data is changed, it does not leave an imprint behind, whereas Windows store files in a index format; ie. "Data Chunk 1, 2, 3 and 4 is file X", while iOS stores it in a compound or data structure.

Even if you could find a software to do this (there's quite a few out there), the data may be scrambled from the writing of other sectors in your phone's memory, making it unreadable.

Side note: Pictures and music are stored in a different structure to apps.

"but i can still try my ipad isnt jailbreaked, can say please a few of the data retriver programs i still want to try" – Eric
Can I recover my deleted world?

There are many software out there that do this. But sadly - None are free (that I could find).
All I can suggest is use the trials for them. They should have trial versions anyway, but watch out for the restrictions that the trials have (apart from the simple time limit).

Recovering is very simple.
Just plug in your device, let the program detect for "deleted files" and then choose what to recover.

Some programs you can use:

http://www.freeiphonedatarecovery.com (free version of FiPR)
http://www.aiseesoft.com/iphone-data-recovery/
http://www.leawo.org/ios-data-recovery/
http://www.datarecoveryforiphone.com/ios-data-recovery.html

Alternatively, restoring an earlier backup of your iOS device should also work as iTunes (on default) backs up your phone every time you upload new apps/songs/whatever to it... Unless you don't have a backup that was created close to (but still before) the world was deleted.