I need to see the processes that were running on my systems (Ubuntu, OpenWRT, Fedora) at a specific time. The only way that I am aware of is "ps" which gives me a current snapshot.
You may be able to find something in /var/log/messages. Many applications will output a message when they start. Other than that, process starts are not logged by default.
You can however use applications that will log such information. auditd is one option, but may be somewhat overkill for your need. A simpler monitoring tool would be acct. Upon installing and start acct, you can use the command sa to get a list of which processes were started by which users at which time.