var defaultEvents = [
  {
    // Just an event
    title: 'Long Event',
    start: '2017-02-07',
    end: '2017-02-10',
    className: 'scheduler_basic_event'
  },
  {
    // Custom repeating event
    id: 999,
    title: 'Repeating Event',
    start: '2017-02-09T16:00:00',
    className: 'scheduler_basic_event'
  },
  {
    // Custom repeating event
    id: 999,
    title: 'Repeating Event',
    start: '2017-02-16T16:00:00',
    className: 'scheduler_basic_event'
  },
  {
    // Just an event
    title: 'Lunch',
    start: '2017-02-12T12:00:00',
    className: 'scheduler_basic_event',
  },
  {
    // Just an event
    title: 'Happy Hour',
    start: '2017-02-12T17:30:00',
    className: 'scheduler_basic_event'
  },
  {   
    // Monthly event
    id: 111,
    title: 'Meeting',
    start: '2000-01-01T00:00:00',
    className: 'scheduler_basic_event',
    repeat: 1
  },
  {
    // Annual avent
    id: 222,
    title: 'Birthday Party',
    start: '2017-02-04T07:00:00',
    description: 'This is a cool event',
    className: 'scheduler_basic_event',
    repeat: 2
  },
  {
    // Weekday event
    title: 'Click for Google',
    url: 'http://google.com/',
    start: '2017-02-28',
    className: 'scheduler_basic_event',
    dow: [1,5]
  }
];
// Any value represanting monthly repeat flag
var REPEAT_MONTHLY = 1;
// Any value represanting yearly repeat flag
var REPEAT_YEARLY = 2;
    
$('#calendar').fullCalendar({
  header: {
  left: 'prev,next today',
  center: 'title',
  right: 'month,agendaWeek,agendaDay'
 },
  editable: true,
  defaultDate: '2017-02-16',
 eventSources: [defaultEvents],
  dayRender: function( date, cell ) {
    // Get all events
    var events = $('#calendar').fullCalendar('clientEvents').length ? $('#calendar').fullCalendar('clientEvents') : defaultEvents;
  // Start of a day timestamp
    var dateTimestamp = date.hour(0).minutes(0);
    var recurringEvents = new Array();
    
  // find all events with monthly repeating flag, having id, repeating at that day few months ago  
    var monthlyEvents = events.filter(function (event) {
      return event.repeat === REPEAT_MONTHLY &&
        event.id &&
        moment(event.start).hour(0).minutes(0).diff(dateTimestamp, 'months', true) % 1 == 0
    });
    
    // find all events with monthly repeating flag, having id, repeating at that day few years ago  
    var yearlyEvents = events.filter(function (event) {
      return event.repeat === REPEAT_YEARLY &&
        event.id &&
        moment(event.start).hour(0).minutes(0).diff(dateTimestamp, 'years', true) % 1 == 0
    });
    recurringEvents = monthlyEvents.concat(yearlyEvents);
    $.each(recurringEvents, function(key, event) {
      var timeStart = moment(event.start);
      // Refething event fields for event rendering 
      var eventData = {
        id: event.id,
        allDay: event.allDay,
        title: event.title,
        description: event.description,
        start: date.hour(timeStart.hour()).minutes(timeStart.minutes()).format("YYYY-MM-DD"),
        end: event.end ? event.end.format("YYYY-MM-DD") : "",
        url: event.url,
        className: 'scheduler_basic_event',
        repeat: event.repeat
      };
   
      // Removing events to avoid duplication
      $('#calendar').fullCalendar( 'removeEvents', function (event) {
          return eventData.id === event.id &&
          moment(event.start).isSame(date, 'day');      
      });
      // Render event
      $('#calendar').fullCalendar('renderEvent', eventData, true);
    });
  }
});
#calendar {
 width: 100%;
 margin: 0 auto;
}
<!DOCTYPE html>
<html>
<head>
  
  <meta charset="utf-8">
  <meta name="viewport" content="width=device-width">
  <title>JS Bin</title>
  <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/fullcalendar/3.1.0/fullcalendar.css" />
</head>
<body>
<script src="https://cdn.jsdelivr.net/momentjs/2.14.1/moment-with-locales.min.js"></script>
<script src="https://code.jquery.com/jquery-2.1.4.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/fullcalendar/3.1.0/fullcalendar.js"></script>
  <div id='calendar'></div>
</body>
</html>