use strict;    # always...
use Bio::SeqIO;

my $bigfasta = "bigfasta.faa";
my $seqin = Bio::SeqIO->new(-file => $bigfasta, -format=>"fasta");

while ($inseq = $seqin->next_seq) {
        my $id = $inseq->display_id;
        my $outfile = "$id.fasta";
        my $seqout = Bio::SeqIO->new(-file=>">$outfile", -format=>"fasta");
        $seqout->write_seq($inseq);

}