A "disk utility" for an operating system that does not have a Finder or file system in the conventional sense is a non-starter. iOS sandboxes everything to the max and data files are encapsulated in the creating app's sandbox. Even iCloud retains a semblance of that data isolation in the way it handles iOS app files.
However, when things get wonky try pressing and holding the on/off button and the home button until the screen blanks and the white Apple appears on the screen. Release the two buttons and wait patiently until the system resets. This is a non-destructive process and not the same as shutting down and then booting. There are reset options in Settings > General but most of those are at least partially destructive and require resetting lots of stuff.
Last edited by joemikeb; 10/18/15 09:36 PM. Reason: typo
