Does a mobile phone app have the ability to control the output current?
I assume the question is whether a mobile phone's USB port, when in USB host mode (and therefore supplies the VBUS), has any ability to control the output.

The answer is NO, USB VBUS provides fixed 5 V output, with optional current limit either at 100/150 mA (if the device is designated as "low-power USB host"), or at 500/900 mA if manufacturer elected to sacrifice its battery life and designates the phone as "high-power host". 

The USB framework doesn't define any means to control or regulate VBUS output power other than shut it off due to overcurrent (which is optional). So no mobile APP can do this job. If you want to control a fan with variable speed, you need to design some external circuitry for that.