You can hold the Home and Power button for about 10 seconds until iPhone restarts itself. In many cases, this hard reset to reboot iPhone in blue screen of death can work.
You can restore iPhone with iTunes when your device is in blue screen of death. But it will erase all data and settings on iPhone. If you have backed up iPhone previously, have a try like this:
Connect iPhone to computer > turn off iPhone by holding down Power and Home buttons for 10 seconds > release Power button but keep holding Home button until the computer beeps > when iTunes opens, click the iPhone icon, go to Summary, and click "Restore" > follow the prompts.
There is an excellent program called ReiBoot. It is the freeware and you can use it to restart your iPhone in blue screen of death. It will never cause any data loss or damage to your iPhone.
Download and install ReiBoot on your Windows PC (Windows 10/8.1/8/7/XP/Vista). Mac users go to ReiBoot for Mac and it works on Mac OS X 10.10 Yosemite, 10.9/10.8/10.7/10.6.
http://www.any-data-recovery.com/tips/iphone/iphone-blue-screen-of-death.html
Whose your provider?
http://www.forbes.com/sites/amitchowdhry/2015/06/25/t-mobile-iphone-users-are-ex periencing-blue-screen-of-death-issues/