Rsa97

function getFreeInterval($intervals, $startTime, $endTime)
{
    $result = [];
    $ok = false;
    foreach($intervals as $key => $interval){
        list($start, $end) = explode('-', $interval);
        if ($startTime >= $start && $endTime <= $end) {
            $ok = true;
            if ($startTime > $start) {
                $result[] = "{$start}-{$startTime}";
            }
            if ($endTime < $end) {
                $result[] = "{$endTime}-{$end}";
            }
        } else {
            $result[] = $interval;
        }
    }
    return [
        $ok,
        $result
    ];
}

$intervals = [
  '09:30:00-13:15:00',
  '14:00:00-17:00:00'
];

list($ok, $result) = getFreeInterval($intervals, '09:30:00', '10:15:00');

var_dump($ok, $result);

// bool(true)
// array(2) {
//   [0]=> string(17) "10:15:00-13:15:00"
//   [1]=> string(17) "14:00:00-17:00:00"
// }

CURLOPT_HEADER
true для включения заголовков в вывод.

usort(
  $array,
  function ($a, $b) {
    return $a['sort'] - $b['sort'];
  }
);

SELECT `person_1`
  FROM `table`
  WHERE `person_2` = :id
UNION SELECT `person_2`
  FROM `table`
  WHERE `person_1` = :id