Applying my powers of guesswork - do you want something like this:

use strict; use warnings;
my @articleid = sort {&byletterandnumber} qw(b1 b2 b3 a100 a5 a8 a10 a
+11);

use Data::Dumper;
print Dumper(\@articleid);

sub byletterandnumber {
    my($aletter, $anumber, $bletter, $bnumber);

  if($a =~ /([a-z]+)(\d+)/){ ($aletter, $anumber) = ($1, $2)}
  if($b =~ /([a-z]+)(\d+)/){ ($bletter, $bnumber) = ($1, $2)}

   return ($aletter cmp $bletter) || ($anumber <=> $bnumber);
}
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Edit: this sorts firstly by the letter part, and then by the number part, giving a5, a8, a10, a11, a100, b1, b2, b3 in this case.