No, the sentence "James opened the door of his cluttered refrigerator", is not a fragment.
The first part, James opened the door his cluttered refrigerator, as this part has a main clause: James is the subject; opened is the verb. A fragment will not have a main clause.
A sentence fragment is a sentence which is missing either its subject or its main verb. Here is a beautiful example of a sentence fragment: because of the rain. On it's own, because of the rain doesn't form a complete thought and it also doesn't makes any sense. It leaves us wondering what happened because of the rain.
Basically, the sentence fragment will be like leftover phrase, an abandoned clause or a missing verb or subject in a sentence. These are pieces of the sentences that have become disconnected from the main clause.
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