This paper presents a new form of video on-demand called ?Fragmented Patching?, which enables clients to move around freely even while receiving video. Patching techniques, which greatly reduce the required network bandwidth through multicasting, have potential for on-demand video distribution. However, patch-flow techniques based on unicast data are unsuitable for providing services to mobile clients because of the intricate process required for relatively short unicast flows to individually follow a moving client. In fragmented patching, however, patch flows are sent via broadcasting. In addition, to avoid increasing traffic due to broadcasting, the patch flows are broken down into segments, each of which is aggregated to be shared with as many multiple clients as possible. We compared the two techniques by using mathematical models, which present the average usage of link bandwidth with the traffic intensity (Erlang), and numerical analysis revealed the aggregation effect by segmenting patch flows countervails the increase in traffic caused by broadcasting patch flows.