To implement draggable events in the Mendix CalendarWidget based on FullCalendar, you will need to make some changes to the source code of the widget.
this.calendar = new FullCalendar.Calendar(calendarEl, {
plugins: ['dayGrid', 'timeGrid', 'list'],
defaultView: 'dayGridMonth',
header: {
left: 'prev,next today',
center: 'title',
right: 'dayGridMonth,timeGridWeek,timeGridDay,listMonth'
},
events: this.events,
editable: true
});