convert date and time string from one format to another

Question

I have a date and time string with this date

$old_date = 'Oct 2 10:07:07 2015 GMT';

I would like to convert it to this format

Fri, 02 Oct 2015 10:07:07 +0000

I've tried this but it didn't work:

$old_timestamp = strtotime($old_date);
$new_Date = date('jS F Y H:i A T O', filemtime($old_timestamp));