Query posts by specific word on title

The answer to this question is here.

The full credit of the answer to my question goes for the author of the answer birgire.

All I had to do was slightly change is plugin “Support for post name like in WP_Query” turning it into a function like this:

add_filter( 'posts_where', 'title_like_posts_where', 10, 2 );
function title_like_posts_where(  $where, $q) {
if( $name__like = $q->get( '_name__like' ) )
{
    global $wpdb;
    $where .= $wpdb->prepare(
        " AND {$wpdb->posts}.post_name LIKE %s ",
        str_replace( 
            array( '**', '*' ), 
            array( '*',  '%' ),  
            mb_strtolower( $wpdb->esc_like( $name__like ) ) 
        )
    );
}
return $where;
}

A special thanks to Pieter Goosen for pointing my out to the solution.