Taking from bart's example, you can also make it one line if you wish. I've also replaced the == with eq, as you said you are "trying to check for the occurance of a string/value withing another string". This way you'll be able to manage strings as well as numbers (well... stringified versions of numbers, which in the world of perl is sufficient for this task).

my $string = '13,130,213';
my $check = '13';

if ( grep { $_ eq $check } split(/,/, $string) ) {
    print "'${check}' is in '${string}'\n";
}
else {
    print "'${check}' is NOT in '${string}'\n";
}
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Though if you need to check the string for multiple substring checks, you're better off skipping the one-liner and working off a an array containing the split entities:

my $string = '100,two hundred,300,400,500,600,700,800';
my @checks = ( qw/200 400 600 700 900/ );

my @items = split(/,/, $string);

for my $check (@checks) {
    if ( grep { $_ eq $checks } @items ) {
        print "'${check}' is in '${string}'\n";
    }
    else {
        print "'${check}' is NOT in '${string}'\n";
    }
}
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