Setup DNS Forward Server to forward only specific domains

Question

I want to setup DNS Forwarding Server to forward DNS resolution requests for only specific zones.

I am using the following config.

acl "trusted" {
        localhost;
        10.x.x.x/24;
};

options {
        listen-on port 53 { 10.x.x.x; };
        listen-on-v6 port 53 { ::1; };
        directory       "/var/named";

        allow-query     { trusted; };

        dnssec-enable no;
        dnssec-validation no;
};

zone "forward.example.com" {
        type forward;
        forward only;
        forwarders { 10.x.x.x; };
};

This is forwarding forward.example.com to correct DNS, but it also resolves other URLs. I want DNS Server to forward only for forward.example.com and return nothing for others, so that client uses it's own fallback DNS.