Fixing the email functions and notifications of an application built with PHP5 in LAMP

I need to fix the email notifications of an application build with PHP5 most of the time email don’t go through when people sign up or make a reservation or get an update. I can see the error logs in the server of the copy of the emails but no one receive email… (Budget: $50 – $100 USD, Jobs: Apache, JavaScript, Linux, MySQL, PHP)