Checking file modification date for a local file against a web hosted file

Question

I've get the file modification date for a local file with this code

<?php 
    $filename = 'db/ciupercomania.db';
    if (file_exists($filename)) {
        echo "This database was created on: <b>".date("F d Y H:i:s.", filemtime($filename)) . "</b><br/><br/>";
    } else {
        echo "File not exist.";
    }
?>

but I'm struggling to get it for a dropbox hosted file, where I use this code:

<?php
    $filename = 'https://www.dropbox.com/home/ciupercomania/Android_db?preview=Ciupercomania.db';
    if (file_exists($filename)) {
        echo "Out there is a database created on: <b>".date("F d Y H:i:s.", filemtime($filename)) . "</b><br/><br/>";
    } else {
        echo "File not exist.";
    }
?>

I want to mention that I tried filectime as well as the dropbox link with extension ?dl=0 and ?dl=1 (automatic or by choice download) without success.

For the dropbox link I always get the FILE NOT EXIST message. If I don't echo it, I get a warning: Warning: filemtime(): stat failed for https://www.dropbox.com/home/ciupercomania/Android_db?preview=Ciupercomania.db

---

Edit

Based on ADyson observation and his provided links, combined with other searches on this theme. I found out that filemtime() only works with files on the same server, and I should look for other solutions like curl_getinfo() or get_header(). Based on that I'm tried these codes:

<?php
  $url = 'https://www.dropbox.com/home/ciupercomania/Android_db?preview=Ciupercomania.db';
  $curl = curl_init($url);

  //don't fetch the actual page, i only want headers
  curl_setopt($curl, CURLOPT_NOBODY, true);

  //stop it from outputting stuff to stdout
  curl_setopt($curl, CURLOPT_RETURNTRANSFER, true);

  // attempt to retrieve the modification date
  curl_setopt($curl, CURLOPT_FILETIME, true);

// disabling SSL verification to a HTTPS website, I don't care about it.
//  curl_setopt($curl, CURLOPT_SSL_VERIFYHOST, 0);
//  curl_setopt($curl, CURLOPT_SSL_VERIFYPEER, 0);

  // disabling SSL verification for a HTTPS website, I don't care about it.
  curl_setopt($curl, CURLOPT_SSL_VERIFYHOST, false);
  curl_setopt($curl, CURLOPT_SSL_VERIFYPEER, false);

//Tell cURL where my certificate bundle is located.
//  $certificate = "cert/cacert.pem"; 
//  curl_setopt($curl, CURLOPT_CAINFO, $certificate);
//  curl_setopt($curl, CURLOPT_CAPATH, $certificate);

  //Check for errors.
  if(curl_errno($curl)){
    throw new Exception(curl_error($curl));
  }

   $result = curl_exec($curl);

//  if ($result === false) {
//   die (curl_error($curl));
//  }

  $timestamp = curl_getinfo($curl, CURLINFO_FILETIME);
  if ($timestamp != -1) {  //otherwise unknown
    echo date("Y-m-d H:i:s", $timestamp); 
  } 
?>

and this one

<?php
  $url = 'https://www.dropbox.com/home/ciupercomania/Android_db?preview=Ciupercomania.db';
  $h = get_headers($url, 1);

  $dt = NULL;
  if(!$h || strpos($h[0], '200') !== false){
    $dt = new \DateTime($h['Last-Modified']);
    echo $dt;
  }
?>

First I've got SSL verification error and for that I tried both, ignoring it with CURLOPT_SSL_VERIFYHOST, false or CURLOPT_SSL_VERIFYHOST, 0, or by pointing at it with:

$certificate = "cert/cacert.pem"; 
curl_setopt($curl, CURLOPT_CAINFO, $certificate); 

but without any success. I don't receive errors but neither a result.

Returning at ADyson's observation and since I'm really dumb, I would really appreciate it, if someone can point me to where I'm doing wrong and help me out.