GlideAjax is supported in Client Scripts in Service Portal, but it is not currently supported in the Client Controller of a Widget. Script Include functions are only accessible in the Server Script of the widget.
The Community post below describes how to create a Script Include that can be used in any widget's server script for specific applications.
The class object can be directly initialized without using GlideAjax. Client script calling Server Script method is possible using c.server.get.