I'm new both to Laravel and PHP. I'm wondering why some sub-directories in Laravel application have files with first letter in uppercase and others in lowercase. Why this "inconsistency"?
According to the PSR-4 convention:
http://www.php-fig.org/psr/psr-4/
So that defines your name spaces. The convention is to match your directory names to your namespaces. If this were java, they'd all be lower case. However, in PHP, the namespace convention is to keep them all upper case. The other convention is that your namespace should match your directory structure for non third party code. However do keep in mind that with psr-4 this is not required.