Can I update my iPhone through my phone without using a computer system

Yes, as long as your phone is eligible to be updated, your battery is higher than 50% and you are connected to Wifi, you can update over the air. See how in this link --> Update your iPhone, iPad, or iPod touch - Apple Support

You can update with a WiFi network connection. Start here: https://support.apple.com/en-us/HT204204

Umeshv1989 wrote:

Yes you can try using itunes to update your mobile

Read the OP again. They asked how to update through their phone WITHOUT using a computer. To update via iTunes, requires a computer.

Yes you can try using itunes to update your mobile