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• We develop a new finite-time method for controlling and synchronising fractional-order financial systems • A Deep Learning Recurrent Neural Network is integrated by terminal sliding mode control • The proposed technique is applied to a chaotic fractional-order financial model with market confidence under highly complex and time-varying uncertainties • It is shown comparatively that when the disturbances are high, the conventional TSMC methods fail Disturbances are inevitably found in almost every system and, if not rejected, they could jeopardize the effectiveness of control methods. Thereby, employing state-of-the-art observers could improve the reliability and performance of controllers dramatically. Motivated by this, we develop a new finite-time method for controlling and synchronising fractional-order systems. The deep learning recurrent neural network, which is a strong tool in handling highly complex and time-varying uncertainties, is integrated by terminal sliding mode control. On the basis of Lyapunov stability theorem, the finite-time convergence and stability of the closed-loop system are proven. Then, the proposed technique is applied to a chaotic fractional-order financial model with market confidence. In simulations, it is supposed that the system is operating in the presence of complex disturbances. The results of the proposed technique are compared with terminal sliding mode control. Numerical results illustratively confirm the theoretical claims about the robust performance of the deep learning control technique. Also, it is shown that when the disturbances are high, the conventional methods fail. [ABSTRACT FROM AUTHOR]