Bluetooth radio control of a motor
You may want to have a look at the Adafruit BLE modules:
https://learn.adafruit.com/introducing-the-adafruit-bluefruit-le-uart-friend/bleuart?view=all

They have provided great examples of how to connect from Android and iOS devices, as well as providing apps or code to integrate into your own apps and you get to implement the motor controller code yourself on the Arduino so should have full control over that side.

They even have an example where they are controlling a motor using an Arduino and Bluetooth, it may not be exactly what you need but hopefully gets you closer to an answer:
https://learn.adafruit.com/bluetooth-motorized-camera-slider/overview?view=all