Will it erase some of my application when i upgrade from ios 6.0 to ios 6.1.3?
Will it erase my application when upgrading to ios 6.1.3 from ios 6.0?
Your apps and settings shouldn't be deleted by an iOS upgrade. If you do the upgrade through iTunes on OS X or Windows as is typical, you'll get a backup as part of the iOS upgrade, and — if you're asking this question — you probably want a backup anyway. That backup is how you can recover from an iOS upgrade failure, or from the loss or theft of your iOS device.