How to keep alive a PHP session using (client-side) cookies?

Question

Sounds like a basic question, but after hours of research I still have nothing to solve the problem.

I'd like a simple thing: keep users logged in on my website for longer than 24 minutes.

My site runs on an apache server and shared hosting, I do not have access to edit the php.ini file.

Messing around with (session.gc_maxlifetime) did not work.

I'm looking for a cookie-based solution at this point - a cookie that is stored on the client side, and is deleted at logout. So PHP would not destroy the session despite of inactivity if this cookie is present.

Is this possible?

(I'm running a site with long articles, so users may be considered 'inactive' by the server and be logged out when they click for the next article. That's what is happening now.)