current_user_can( ‘edit_post’, $post_id ) does not work for contributer but for administrator

I have a custom post type named project which has

'capability_type' => 'post'

while registering using register_post_type.

In my theme files and also functions.php file, I have situations where I should check if the project to be edited is authored by the user or not.

So I use this:

if ( !current_user_can( 'edit_post', $porject_id ) ) return;

where $project_id is post id of the project to be edited.

For example I have a page template named single_project.php where I can show single posts in project post type to users and I want these people can see each project single page:

1. administrators
2. editors
3. the contributer (post author)

but using the above code, It is ok with administrators and editors, while not for the contributer himself!

When I use:

var_dump( current_user_can( 'edit_post', $project_id ) )

with the contributer logged-in account, it returns

false

while

var_dump( current_user_can( 'edit_posts' ) )` (with trailing `'s'`)

returns

true
(but for every post, not just does for him).

Any help with this?

using map_meta_cap I added edit_post per post cap to user

function my_map_meta_cap( $caps, $cap, $user_id, $args ){
    if ( 'edit_post' == $cap ) {
        $post = get_post( $args[0] );
        $post_type = get_post_type_object( $post->post_type );
        $caps = array();
        if ( $user_id == $post->post_author )
            $caps[] = $post_type->cap->edit_posts;
        else
            $caps[] = $post_type->cap->edit_others_posts;
    }
    return $caps;
}
add_filter( 'map_meta_cap', 'my_map_meta_cap', 10, 4 );