The party applying for the writ of partition shall give the other parties concerned at least 20 days' notice of his intention to make the application. If any of the other parties is a minor, a mentally ill or retarded person, or a beneficiary of a trust, the 20 days' notice shall be served on the guardian of such minor, the guardian of such mentally ill or retarded person, or the trustee of such beneficiary. If any of the parties reside outside of this state, the court may order service by publication as in its judgment is right in each case.