You can use your FBO to maintain your aircraft.

To do so, your FBO needs to have Workshop Agreements for the aircraft class you want to work on.

Level 1 workshops let you handle basic maintenance for your aircraft (engine repair, airframe repair, 100h inspection)
Level 2 workshops let you handle advanced maintenance (annual checkup and engine replacement)

Even with your own FBO, you need to pay for the aircraft parts that need to be replaced.
The point of owning a FBO is to pay the minimal amount for your aircraft maintenance (always with markup 1.0)

You can set the markup of your FBO greater than 1.0, it will then be used if any other player uses your workshop for maintenance.

Note that your FBO will always be able to process any aircraft even without the Workshop Agreements by calling a maintenance truck to do the work. It is way more expensive.