$_GET the variable of javascript to php

If you want the literal index full_val, then use it in the query string:

data: 'full_val='+add,

So that in PHP, you'd be able to use $_GET['full_val']

Alternatively, you could also put an object in that field:

data: {full_val: full_val, add: add},

Here is the description:

data
Type: PlainObject or String or Array
Data to be sent to the server. It is converted to a query string, if not already a string. It's appended to the url for GET-requests.

Your data just has the values and does not have the keys. See below for how to pass the keys and values.

add = 'request';
full_val = 'barrack obama';
$.ajax({
    url: 'plugins/add_friend.php',
    data: {full_val:full_val,add:add},
    success: function(data)
    {

    }
});

In your PHP use $_GET['full_val'];

send your values with data parameter correctly and add type:get to define GET method

add = 'request';
full_val = 'barrack obama';
$.ajax({
  type: "get",
  url: 'plugins/add_friend.php',
  data: {'full_val':full_val,'add':add},
  success: function(data) {

  }
});

Then you will get values on php :-

use $_GET['full_val'] rather $_GET[full_val]

Try Using this

add = 'request';
full_val = 'barrack obama';
$.ajax({
        url: 'add.php',
        data: 'full_val='+add,
        success: function(data)
        {
           alert(data);
        }
        });

You can use the .get() method. The variables you can set using an object literal. For example:

$.get("/plugins/add_friend.php", {
    add:  "request",
    full: "Barrack Obama"
}).done(function(data) {
    console.log("Status:", data.status);
    console.log("Received:", data.received);
});

And the PHP could be done something like this:

$add  = filter_input(INPUT_GET, 'add', FILTER_SANITIZE_STRING);
$full = filter_input(INPUT_GET, 'full', FILTER_SANITIZE_STRING);
echo json_encode(array(
    'status': 'OK',
    'received': "{$add} and {$full}",
));