If it is a date range only for Posting date, then you must have two fields in your search bar referring to Posting date.
The filter for the first one could be Greater or equal and for the second one could be smaller or equal.
I see you are using two dates. So, if you want to support two date ranges, then I guess you need four search filters.
I am not sure if there are any appstore widgets available for this. But above is how we could do this out of box.