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• In this paper, we present a new fractional-order hyperchaotic memristor oscillator. • The proposed system has been investigated through numerical simulations. • A novel robust adaptive controller is implemented to synchronize the system. • As an application, the system has been implemented for voice encryption. The present study proposes a new fractional-order hyperchaotic memristor oscillator. The proposed system is studied through numerical simulations and analyses, such as the Lyapunov exponents, bifurcation diagrams, and phase portraits. Then, using the sliding mode concept, a robust adaptive control scheme is designed to synchronize the proposed system. The adaptation mechanism is implemented to estimate the unknown parameters of the slave system. Then, the output of the proposed adaptation mechanism is used for the control scheme. The stability of the closed-loop system is proven via a fractional version of the Lyapunov stability theorem and Barbalat's lemma. Numerical simulations of synchronization are shown to investigate the performance of the developed control technique on the uncertain fractional-order hyperchaotic memristor oscillator. Finally, as an engineering application, the proposed fractional-order system is implemented for voice encryption. In this regard, to show the appropriate performance of the proposed system for voice encryption, statistical characteristic of the encryption and decryption processes are performed through different methods including correlation, entropy, root mean square, and root sum of squares. [ABSTRACT FROM AUTHOR]