$('.fc-next-button').click(function() {
    var month = $("#month").val();
    var nextMonth = ++month;
    $.ajax({
            url: 'controllerName/getNextMonthEvents',
            type: 'POST',
            data: {
                nextMonth: nextMonth
            },
            success: function(nextEvents) {
               var nextResult1 = $.parseJSON(nextEvents);
            $('#event_calendar').fullCalendar({
               header: {
                       left: 'prev,next today',
                       center: 'title',
                       right: 'listDay,listWeek,month'
               },
               defaultView: 'month',
                editable: true,
                eventLimit: true, // allow "more" link when too many events
                events: nextResult1, //I am displaying my events here
            $("#month").val(nextMonth);
        },
    });
});

My Controller:-
public function getNextMonthEvents() {
        $nextMonth = $_POST['nextMonth'];
        $nextEvents = $this->modelName->getNextMonthEvents($nextMonth);
        echo json_encode($nextEvents);
    }
My view:-
public function getNextMonthEvents($nextMonth) {
        $where = "MONTH(start_date) = $nextMonth";
        $rs = $this->db->select('name as title,DATE(start_date) as start,DATE(end_date) as end')
              ->from('db_name')
              ->where($where)
              ->get()->result();

        return $rs;
    }