JSFiddle - React, Tailwind, and code Playground

HTML

<script src="http://cdn.kendostatic.com/2012.2.710/js/kendo.all.min.js"></script>
<link rel="stylesheet" href="http://cdn.kendostatic.com/2012.2.710/styles/kendo.common.min.css">
<link rel="stylesheet" href="http://cdn.kendostatic.com/2012.2.710/styles/kendo.blueopal.min.css">
<a id='backwardDate' class='k-button' onClick='backwardDate();' title='One day back' href='#'>back</a>
<input id="datepicker" title='Choose date' />
<a id='forwardDate' onClick='forwardDate();' class='k-button' title='One day forward' href="#">forward</a>
<p id='internalDate'>internal date</p>

JavaScript

$(document).ready(function() {
    $("#datepicker").kendoDatePicker({
        value: new Date(),
        format: "dd.MM.yyyy",
        change: function(e) {
            $("#internalDate").text(e.sender.value().toString());
        }
    });
});

window.forwardDate = function() {
    var datePicker = $("#datepicker").data("kendoDatePicker");

    var date = datePicker.value();

    // set new date
    datePicker.value(buildDateString(date, 1));
    datePicker.trigger("change");
}

window.backwardDate = function() {
    var datePicker = $("#datepicker").data("kendoDatePicker");

    var date = datePicker.value();

    // set new date
    datePicker.value(buildDateString(date, -1));
    datePicker.trigger("change");
}
    
function buildDateString(date, diff) {
    // update date object (takes care of month/year changes and daylight saving issues)
    date.setDate(date.getDate() + diff);

    var day = date.getDate() + "";
    if (day.length == 1) {
        day = "0" + day;
    }
    var month = (date.getMonth() + 1) + "";
    if (month.length == 1) {
        month = "0" + month;
    }
    var year = date.getFullYear();

    return day + "." + month + "." + year;
}