Calculate Appointments beetween two dates - php

Question

Situation:
I have arrays with information of the used appointments and the calculated days for the new appointment series based on PHP.
For example, the exist appointment array:
Array
(
[0] => Array
(
[date] => 2019-05-02
[time_start] => 14:00:00
[time_end] => 15:30:00
)
[1] => Array
(
[date] => 2019-05-06
[time_start] => 14:00:00
[time_end] => 15:30:00
)
)
Now, i will check have the calculated series (same array format) collisions with the exist appointments.
My Question:
How can i check if a collision exist beetween the start and end time and if yes how i can give the array a new value with a time windows after or before the exist appointment. This within a time windows from 08:00 am to 4:00 pm.
What i have is the calculation of the appointment days.
private function calculate_dates($data, $measure)
{
$this->load->model('calendar/calendar_model');
$holiday_dates = $this->calendar_model->get_holidays();
foreach ($holiday_dates as $key => $value) {
$holidays[] = $value['holiday_date'];
}
$begin = new DateTime($data->measure_begin);
$end = new DateTime($data->measure_end);
$oneday = new DateInterval("P1D");
$days = json_decode($data->measure_dates);
$wdays = array();
$ue_minutes = 0;
$minutes = ($data->measure_ue * $measure->ue_minutes/2);
$daterange = new DatePeriod( $begin, DateInterval::createFromDateString('+1 weekdays') ,$end );
foreach(new DatePeriod($begin, $oneday, $end->add($oneday)) as $day) {
$day_num = $day->format("N"); /* 'N' number days 1 (mon) to 7 (sun) */
if($day_num < 6 ) { /* weekday */
$wdays[] = $day;
}
}
$count = 1;
foreach($wdays as $date){
foreach ($days as $key => $value) {
if(mb_strtolower($date->format('l')) == $value){
if(($data->measure_ue/2)+1 != $count){
if(in_array($date->format('Y-m-d'), $holidays)) {
$dates[] = $this->close_days($date, $days, true)->format('l, d.m.Y');
} else {
$dates[] = $date->format('l, d.m.Y');
}
$count++;
}
}
}
}
return array(
'dates' => $dates,
'minutes' => round($minutes/count($dates))
);
}
private function close_days($date, $days, $init = false)
{
if($init){
$days[] = 'saturday';
$days[] = 'sunday';
}
if( in_array(mb_strtolower($date->format('l')), $days) ) {
$this->close_days($date->modify('next day'), $days);
}
return $date;
}
Any Ideas for a solution or maybe a code for a better way?