Maybe this could also help.
I would rather take the start and end from the CLI and check if they are correct.
See if this can help:

#!/usr/bin/perl -w
use strict;
use Getopt::Long;

GetOptions(
    'directory=s'  => \my $directory,
    'start_date=s' => \my $start,
    'end_date=s'   => \my $end,
);

die 'Unknown directory path'
  unless defined $directory;

opendir DIRH, $directory or die "can't open directory :$!";
my @files = grep { -d && $_ ne '.' && $_ ne '..' } readdir(DIRH);
closedir DIRH or die $!;

@files = file_range(
    files => \@files,
    begin => $start,
    end   => $end,
);

for (@files) {
  # do whatsoever you want in here 
  # to each of the directory, you might have to 
  # use subroutrine chdir, then opendir
  # over to you     
    print $_, $/;
}

sub file_range {
    my %data      = @_;
    my $file_size = 0;
    # check if the dates each has date in full i.e 4 digit 20110910
    $file_size += split //, $_ for $data{begin}, $data{end};    #== 16
+;

    die 'One or both of your start or end date is not correct '
      unless $file_size == 16;

    my @files_to_return;

    for my $file ( sort { $b <=> $a } @{ $data{files} } ) {
        push @files_to_return => grep /$file/, $data{begin} .. $data{e
+nd};
    }

    return @files_to_return;
}
[download]

To run so: script.pl -directory . -start 20110219 -end 20120303 Where '.' is your directory, you can as well change that.