Thanks Dmit OE,
Your guess would be correct, jquery.mobile might conflict against default jquery in OE.

Therefore, I resolve this issue using jquery ui instead of jquery mobile as following,

//in Header of BaseLayer
<link href="https://code.jquery.com/ui/1.10.4/themes/ui-lightness/jquery-ui.css" rel="stylesheet">
<script src="https://code.jquery.com/ui/1.10.4/jquery-ui.js"></script>
<script>
$( function() {
    $( "#Rslider" ).slider({
        range:"max",
        min:0,
        max:100,
        step:0.5,
        value:50,
        slide: function( event, ui ) {
            $( ".Rrange input" ).val( ui.value );
        }
    });
    $( ".Rrange input" ).val( $( "#Rslider" ).slider( "value" ) );
} );
</script>

//in Body of SubLayer
Text Input Field form with Custom Classes="Rrange"

Now, I need to connect this value to Database to get, update.....a lot of job....

Thanks,

Yes, I have tried it.

1) When I remarked this line, the result was same.

P.S. You shoudl remove this linefrom your code:

<script src="https://code.jquery.com/jquery-1.11.3.min.js"></script>

Dmit OE, Thank you so much! I will try it.