Javascript Slider with Multiple Allowed sections/timeslots

I want to implement a time-slot selector in jquery/javascript slider form.

There are a few slider libraries out there such as Ion Slider, jQRangeSlider etc. but I don't know how I would be going about this. It doesn't look like they support multiple "dead-zones".

I want the user to be able to select a timeslot (from and to) during a particular day. To select the day, I have implemented a date picker, then for the date, I retrieve the already occupied slots for instance:

07h00 - Available
07h30 - Available
08h00 - Occupied
08h30 - Occupied
09h00 - Occupied
09h30 - Available
...
18h30 - Available
19h00 - Available

So the range picker must look like this:

The user should only be able to select a time zone in the available sections (blue) and drag the start slider between the "available" section, and the end selector will move along with it. There might be multiple unavailable zones (Red).

Is this possible with the libraries already out there or is this a case of roll my own?

I have thought about using a bunch of check boxes then check all the boxes between the start and end time-slots, and disable the already occupied slots, but I think a slider like this would be much more user friendly to use, functionally and visually.

I have decided to implement an ionRangeSlider with custom slots from 05h30 to 19h30. A separate array of used time-slots to which I compare in the onChange event.

var slider = $("#timeslotSlider").ionRangeSlider({
    type: "double",
    grid: true,
    from: 1,
    from_value: "06h00",
    to: 2,
    to_value: "06h30",
    values: timeslotvalues,
    onChange: function (data) {
        timeslotSetSelectedText(data);
    }
});

var sliderdata = slider.data("ionRangeSlider");
var dt = sliderdata.result.from_value != null ? sliderdata.result : sliderdata.options;

timeslotSetSelectedText(dt);

The timeslotSetSelectedText function compares the selected range to the used slots then display a message "Available" or "Overlaps Existing time-slot"

The same function is used to Validate the selected slot before sending it to the server.