Since various other solutions have been posted, and you haven't been exactly clear in your requirements, here I use a parser, Mojo::DOM, and Mojo::File for reading/writing. There's more than one way to do it, other parsers exist (XML::Twig etc)...

source.xml

<inline-formula id="ieqn-1"><alternatives><mml:math display="inline"><
+mml:mi>&#964;</mml:mi></mml:math></alternatives></inline-formula>

<inline-formula id="ieqn-2"><alternatives><mml:math display="inline"><
+mml:mi>&#964;</mml:mi></mml:math></alternatives></inline-formula>

<inline-formula id="ieqn-3"><alternatives><mml:math
display="inline"><mml:mi>&#964;</mml:mi></mml:math></alternatives></in
+line-formula>
[download]

1226654.pl

#!/usr/bin/perl

use strict;
use warnings;
use Mojo::DOM;
use Mojo::File;

# read the xml file
my $source = Mojo::File->new( 'source.xml' );
my $xml = $source->slurp;

# use Mojo::Dom to parse the XML
my $dom = Mojo::DOM->new->xml(1)->parse( $xml );

# for each inline-formula id in the file
for my $e ( $dom->find('inline-formula[id]')->each ){
  # create file named value_of_id.mml
  my $file = "$e->{id}.mml";
  my $path = Mojo::File->new( $file );
  # write contents to file
  $path->spurt( $e->to_string );
}
[download]

output

-rw-rw-r-- 1 marto marto  131 Dec  4 10:17 ieqn-3.mml
-rw-rw-r-- 1 marto marto  131 Dec  4 10:17 ieqn-2.mml
-rw-rw-r-- 1 marto marto  131 Dec  4 10:17 ieqn-1.mml
marto@Shemp:~/code/perlmonks$ cat ieqn-1.mml 
<inline-formula id="ieqn-1"><alternatives><mml:math display="inline"><
+mml:mi>&#964;</mml:mi></mml:math></alternatives></inline-formula>
marto@Shemp:~/code/perlmonks$ cat ieqn-2.mml 
<inline-formula id="ieqn-2"><alternatives><mml:math display="inline"><
+mml:mi>&#964;</mml:mi></mml:math></alternatives></inline-formula>
[download]