The code below uses firefox (or mozilla if you swap the commented lines around) to open the url in an already running copy, or open a new instance if it is not already running.
Debian has a www-browser object which normally points to firefox, dunno if fedora has a similiar setuo.
Code:
#!/bin/bash
#
# mozilla=/usr/bin/mozilla
mozilla=/usr/bin/firefox
if ( $mozilla -remote "ping()" &> /dev/null );then
$mozilla -remote "openurl(http://www.google.com, new-tab)" &
else
$mozilla http://www.google.com &
fi
