First of all, we must identify the appositive phrase: an appositive phrase is two or more words standing as a single unit without a subject or a verb, whose function is to rename, re-identify or describe a noun placed right beside it. In the sentence, “Julian” is the appositive because it renames the noun “My youngest brother.”
This appositive is nonrestrictive because, in contrast with restrictive appositives, it is not essential to the meaning of the sentence (If we had to remove “Julian” from the sentence, it would not affect the sentence's meaning) and it is enclosed by commas.