Doing the below initialization doesn't get my desired result.

You're essentially doing @array = ( "string" ); </C> The operator, is double quotes "", you want to use the range operator, so

my $range = "1..3,7..9";
my @array;
while($range =~ /(\d+)\.\.(\d+)/g ){
    my( $left , $right ) =  ( $1, $2 );
    push @array, $left .. $right;
}
print "@array\n";
__END__
1 2 3 7 8 9
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"1..3,7..9" is data and 1..3,7..9 is code