I have ipad mini and iphone 4 and i want to transfer some music from ipad to iphone. Is it possible to use Airdrop?
No, the hardware radio doesn't work in the manner needed for AirDrop to function.
See the fine print of http://www.apple.com/ios/whats-new/#airdrop which states:
AirDrop is available on iPhone 5 or later, iPad (4th generation), iPad mini, and iPod touch (5th generation) and requires an iCloud account
No, you can't use Airdrop with an iPhone 4: http://support.apple.com/kb/ht5887
While your iPad mini supports AirDrop, the your iPhone 4 does not - and as far as I'm aware, music can't be transferred via AirDrop.
That said, for $25/year, you can turn on iTunes Match, which will put a copy of your iTunes library in iCloud, allowing you to access your music anywhere. You can also transfer the music by using a Mac.