Şu kodları bir dene muhtemelen sorun kalmayacaktır, ci kodlarını inceleme fırsatım yok ama yine çalışmazsa buraya is_ajax_request methodunun içeriğini yazarsan net çözümü belirtirim.

function cek_gelsin($sayfam) 
    { 
    $ch = curl_init(); 
    //$ch = curl_init('http://example.com/service/get_video_part');  
    $data = array("video_id" => "$sayfam", "part_name" => "480p", "page" => "0");  
    // "video_id=$sayfam&part_name=480p&page=0"                                                     
    $data_string = json_encode($data); 
    curl_setopt($ch, CURLOPT_URL, 'http://example.com/service/get_video_part'); 
    //cache:false 
    curl_setopt($ch, CURLOPT_HTTPHEADER, array(                                                                           
        'X-Requested-With: XMLHttpRequest',
        'Accept: application/json, text/javascript, */*; q=0.01"', 
        'Content-Type: application/json; charset=utf-8',                                                                                 
        'Content-Length: ' . strlen($data_string))                                                                        
    ); 
    curl_setopt($ch, CURLOPT_SSL_VERIFYHOST, 0); 
    //curl_setopt($ch, CURLOPT_REFERER, 'http://www.cloudflare-watch.org/cgi-bin/cfsearch.cgi'); 
    curl_setopt($ch, CURLOPT_REFERER, 'http://example.com/referer-adress.html'); 
    curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, 0); 
    curl_setopt($ch, CURLOPT_VERBOSE, true); 
    curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1); 
    curl_setopt($ch, CURLOPT_USERAGENT, 'Mozilla/5.0 (Windows NT 6.3; WOW64; rv:34.0) Gecko/20100101 Firefox/34.0'); 
    curl_setopt($ch, CURLOPT_POST, 1); 
    curl_setopt($ch, CURLOPT_CUSTOMREQUEST, "POST");      
    //curl_setopt($ch, CURLOPT_POSTFIELDS, "video_id=$sayfam&part_name=Alternatif+&page=0"); 
    curl_setopt($ch, CURLOPT_POSTFIELDS, $data_string); 
    $exec = trim(curl_exec($ch)); 
    curl_close($ch); 
    return $exec; 
    } 
    $dene="64"; 
    echo cek_gelsin($dene);