Include PHP file in plugin
You can simply load the file normally via php require once 

require_once( __DIR__ . '/resources/DateFormatting.php');
$dataFormatter = new DateFormatting();


From your plugins init function or where ever you would like to call it. 

Edit:

I hope your DateFormatting is not like you posted it because it has no functions. Btw Craft::import() has the advantage that you can import entire folders and it loads the class only to Yiis classmap which means that it is only loaded when you need it and not until then. If you want to use the file for sure, require once is the better way since Craft/Yii does the same in the very end. 

Edit2:

Never mind, Yii uses include and not require_once, sry for the wrong info here. However... today the difference is not that big issue. Comparison include vs require_once