Custom column to represent order - mysql

Question

I am using MySQL to return columns from a data table. What I want to do is use Order By to order the results by a date fields in ascending order and then also return a custom column along with the other desired columns where the custom column represents the index in relation to the Order By results. Right, I have the following query which just returns the desired columns and orders the results:
SELECT
`alert_id`,
`message`,
`expiration`
FROM
`alert`
WHERE
`is_active` = TRUE
ORDER BY
`expiration`
But what I'm having difficulty with is how to also return the custom column that represents the order. So for example, I would like the following (sample data) rows returned:
Pior to Order and Custom Column After the Order and Custom Column
+----------+---------+------------+ +----------+---------+------------+----------+
| alert_id | message | expiration | | alert_id | message | expiration | order_by |
+----------+---------+------------+ +----------+---------+------------+----------+
| 1 | alert1 | 2017-11-20 | | 5 | alert5 | 2017-11-16 | 1 |
| 5 | alert5 | 2017-11-16 | | 6 | alert6 | 2017-11-17 | 2 |
| 6 | alert6 | 2017-11-17 | | 1 | alert1 | 2017-11-20 | 3 |
+----------+---------+------------+ +----------+---------+------------+----------+

Answer 1

With AdrianE's assistance in mentioning the ROW_NUMBER function, even though I am using MySQL and that function is not available, I was able to emulate the function by using the following:
SET #order = 0;
SELECT
`alert_id`,
`message`,
DATE_FORMAT(`expiration`, '%M %D, %Y') AS formatted_date,
(#order := #order + 1) AS order_by
FROM
`alert`
WHERE
`is_active` = TRUE
ORDER BY
`expiration`;