my @sorted =
    map $_->[0],
    sort {
        my $i = 0;
        {
            my $A = $a->[1][$i];
            my $B = $b->[1][$i];
            defined($A) || defined($B)       # Stop if both undef
            and (
                defined($A) <=> defined($B)  # Defined wins over undef
                or (
                    $A !~ /\d/ || $B !~ /\d/ # $A or $B is non-integer
                    ?    (lc $A cmp lc $B)   # ?? Stringy lowercase
                      || (   $A cmp    $B)   #    -> Tie breaker
                    : $A <=> $B              # :: $A and $B are integers
                )
                or ++$i && redo              # tie => next part
            );
        }
    }
    map [ $_, [ split /(\d+)/ ] ], @unsorted;

##</code><code>##

qw(
    bigbang
    x10y
    x9y
    bigboy
    bigBoy
    x11y
)

##</code><code>##

qw(
    bigbang
    bigBoy
    bigboy
    x9y
    x10y
    x11y
)