Yes, you can install it on openstack.

Pivotal Cloud Foundry is a Platform as a Service (PaaS). As a developer, you can deploy application directly to the containers (which are running in openstack VMs) without any knowledge about server configurations. 'cf push' will deploy your application code in a container and gives you a URL to access it. It is pretty easy to handle scale up and down, provides maximum availability to application and it will be taken care by PCF itself.

I found better explanation here as well. https://cloudacademy.com/blog/cloud-f...