It seems that if create_case.php file you create an object of case_controller and want to run the method retrieveAllCaseID but in case_controller.php file you have only a declaration of the function, not the class and method.
If you change your create_case.php file into:
require_once(dirname(__FILE__) . '\..\controller\case_controller.php');
$caseCtrl = retrieveAllCaseID(); //this line is calling the error
there wouldn't be this error. However, they might occur other errors because we don't know what you wanted to do in your application.
I also assume in this answer that there is a typo in "case_cotroller.php file:" - because it should be "case_controller.php file:"