jQuery('#start_date2').datepicker({
    format: '{{ $global->date_picker_format }}',
    autoclose: true,
    todayHighlight: true
}).on('changeDate', function (selected) {
    $('#due_date2').datepicker({
        format: '{{ $global->date_picker_format }}',
        autoclose: true,
        todayHighlight: true
    });
    var minDate = new Date(selected.date.valueOf());
    $('#due_date2').datepicker("update", minDate);
    $('#due_date2').datepicker('setStartDate', minDate);        
});

$(".select2").select2({
    formatNoMatches: function () {
        return "{{ __('messages.noRecordFound') }}";
    }
});

<script src="https://ajax.aspnetcdn.com/ajax/jQuery/jquery-3.4.1.min.js"></script>
<script src="//code.jquery.com/ui/1.9.2/jquery-ui.js"></script>
<link href="//code.jquery.com/ui/1.12.1/themes/base/jquery-ui.css" rel="stylesheet"/>

<input type="text" name="start_date" id="start_date2" class="form-control" autocomplete="off">