Oracle 11g Release 2

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with 
    t(start_date, end_date) as (
        select timestamp '2018-01-01 08:00:00', timestamp '2018-01-01 08:50:00' from dual union all
        select timestamp '2018-01-01 08:15:00', timestamp '2018-01-01 08:20:00' from dual union all
        select timestamp '2018-01-01 08:45:00', timestamp '2018-01-01 09:55:00' from dual union all
        select timestamp '2018-01-01 15:45:00', timestamp '2018-01-01 17:00:00' from dual ),
    r(rn, start_date, end_date) as (
        select row_number() over(order by start_date), start_date, end_date from t ),
    c(rn, start_date, end_date, grp) as (
        select rn, start_date, end_date, 1 from r where rn = 1
        union all
        select r.rn, 
               case when r.start_date <= c.end_date and c.start_date <= r.end_date 
                    then least(r.start_date, c.start_date) else r.start_date end,
               case when r.start_date <= c.end_date and c.start_date <= r.end_date 
                    then greatest(r.end_date, c.end_date) else r.end_date end,
               case when r.start_date <= c.end_date and c.start_date <= r.end_date 
                    then grp else grp + 1 end
          from c join r on r.rn = c.rn + 1)
select min(start_date), max(end_date) from c group by grp

MIN(START_DATE)	MAX(END_DATE)
01-JAN-18 08.00.00.000000000 AM	01-JAN-18 09.55.00.000000000 AM
01-JAN-18 03.45.00.000000000 PM	01-JAN-18 05.00.00.000000000 PM