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Memristor-based oscillators are of recent interest, and hence, in this paper, we introduce a new Wien bridge oscillator with a fractional-order memristor. The novelty of the proposed oscillator is the multistability feature and the wide range of fractional orders for which the system shows chaos. We have investigated the various dynamical properties of the proposed oscillator and have presented them in detail. The oscillator is then realized using off-the-shelf components, and the results are compared with that of the numerical results. A combination synchronization scheme is proposed which uses more than one driver systems to synchronize with one response system. Indeed, we use two different techniques where the first one consists of splitting the transmitted signals into two parts where each part is loaded in different drive systems, while the second one consists of dividing time into different intervals and loading the signals in different drive systems. Such techniques improve the antiattack capability of the systems when used for secure communication.