In Java classes java.util.Date, java.util.Calendar, java.time.LocalDateTime, java.time.LocalDate and java.time.LocalTime  implements comparable interface for natural ordering. We can sort these objects implements comparable interface as below

Collections.sort(List <Date> list);
Collections.sort(List <Calendar> list);
Collections.sort(List <LocalDateTime> list);
Collections.sort(List <LocalDate> list);
Collections.sort(List <LocalTime> list);

Problem occurred when date in String format and following different format pattern as MM/dd/yyyy ‘@’hh:mm a or some more patterns then you have to implement Comparator to sort this date text patterns as below

Collections.sort(dateStrList, new Comparator() {
DateFormat f = new SimpleDateFormat("MM/dd/yyyy '@'hh:mm a"); 

@Override public int compare(String o1, String o2) {
 try { 
   return f.parse(o1).compareTo(f.parse(o2)); 
} catch (ParseException e) { 
throw new IllegalArgumentException(e); 
} 
} }); 

To learn Comparator and Comparable check below link.

Java : Comparable Vs Comparator

In below example you will see sorting of date  in text format and objects also.

Example

package com.date;

import java.text.DateFormat;
import java.text.ParseException;
import java.text.SimpleDateFormat;
import java.time.LocalDateTime;
import java.time.format.DateTimeFormatter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;

public class SortingDateTime {
public static void main(String[] args) {
//java 8
sortDateTimeObject();
sortDateTimeText();
}

private static void sortDateTimeObject() {
List<LocalDateTime>dateTimeList=new ArrayList<LocalDateTime>();
dateTimeList.add(LocalDateTime.of(2012, 05, 12, 5, 16));
dateTimeList.add(LocalDateTime.of(2014, 03, 23, 11, 26));
dateTimeList.add(LocalDateTime.of(2011, 02, 13, 9, 36));
dateTimeList.add(LocalDateTime.of(2013, 11, 12, 5, 16));
dateTimeList.add(LocalDateTime.of(2017, 8, 11, 21, 26));
dateTimeList.add(LocalDateTime.of(2016, 9, 05, 19, 36));

DateTimeFormatter dateTimeFormatter = DateTimeFormatter
				.ofPattern("MM/dd/yyyy '@'hh:mm a");
System.out.println("---> Date & Time Object List Before Sort (MM/dd/yyyy '@'hh:mm a)");
for(LocalDateTime dateTime:dateTimeList)
{
System.out.println(dateTime.format(dateTimeFormatter));
}
// LocalDateTime  internally having Comparable interface no need additional Comparator
Collections.sort(dateTimeList);

System.out.println("---> Date & Time Object List After Sort (MM/dd/yyyy '@'hh:mm a)");
for(LocalDateTime dateTime:dateTimeList)
{
System.out.println(dateTime.format(dateTimeFormatter));
}

}

private static void sortDateTimeText()
{
List<String>dateStrList=new ArrayList<String>();
// MM/dd/yyyy '@'hh:mm a
dateStrList.add("01/21/2014 @03:13 PM");
dateStrList.add("01/21/2011 @04:37 PM");
dateStrList.add("01/21/2012 @10:41 AM");
dateStrList.add("01/21/2013 @10:48 AM");
dateStrList.add("01/22/2015 @06:16 AM");
dateStrList.add("01/22/2013 @06:19 AM");
dateStrList.add("01/21/2018 @05:19 PM");
dateStrList.add("01/21/2013 @05:19 PM");

System.out.println("---> Date & Time List Before Sort (MM/dd/yyyy '@'hh:mm a)");
for(String dateStr:dateStrList)
System.out.println(dateStr);

//Sort String Date
Collections.sort(dateStrList, new Comparator<String>() {
DateFormat f = new SimpleDateFormat("MM/dd/yyyy '@'hh:mm a");
@Override
public int compare(String o1, String o2) {
try {
  return f.parse(o1).compareTo(f.parse(o2));
    } catch (ParseException e) {
      throw new IllegalArgumentException(e);
    }
}
});

System.out.println("---> Date & Time List After Sort (MM/dd/yyyy '@'hh:mm a)");
for(String dateStr:dateStrList)
System.out.println(dateStr);
 }
}

Output

---> Date & Time Object List Before Sort (MM/dd/yyyy '@'hh:mm a)
05/12/2012 @05:16 AM
03/23/2014 @11:26 AM
02/13/2011 @09:36 AM
11/12/2013 @05:16 AM
08/11/2017 @09:26 PM
09/05/2016 @07:36 PM
---> Date & Time Object List After Sort (MM/dd/yyyy '@'hh:mm a)
02/13/2011 @09:36 AM
05/12/2012 @05:16 AM
11/12/2013 @05:16 AM
03/23/2014 @11:26 AM
09/05/2016 @07:36 PM
08/11/2017 @09:26 PM
---> Date & Time List Before Sort (MM/dd/yyyy '@'hh:mm a)
01/21/2014 @03:13 PM
01/21/2011 @04:37 PM
01/21/2012 @10:41 AM
01/21/2013 @10:48 AM
01/22/2015 @06:16 AM
01/22/2013 @06:19 AM
01/21/2018 @05:19 PM
01/21/2013 @05:19 PM
---> Date & Time List After Sort (MM/dd/yyyy '@'hh:mm a)
01/21/2011 @04:37 PM
01/21/2012 @10:41 AM
01/21/2013 @10:48 AM
01/21/2013 @05:19 PM
01/22/2013 @06:19 AM
01/21/2014 @03:13 PM
01/22/2015 @06:16 AM
01/21/2018 @05:19 PM