The main concern of this paper is to address the synchronization problem of chaotic fractional-order fuzzy cellular neural networks (FOFCNNs) through designing the novel adaptive control scheme. The objective of the study is to explore the importance of considering fractional order derivatives (FODs) and time-varying delays. Even though numerous works have been reported in the literature regarding the derivation of sufficient conditions, there has been a lack of research on involving the dynamical analysis of FOFCNNs. Hence, this study focuses on the dynamical analysis of FOFCNNs. Particularly, both asymptotical and exponential synchronization of drive-response FOFCNN model is guaranteed via sufficient conditions that are derived by constructing the fractional Lyapunov functional candidate and solvable linear matrix inequalities (LMIs). Besides that, numerical simulations are performed to reveal the significance of the FODs. Also, an image encryption algorithm is designed based on the chaotic FOFCNNs solutions that result in better security measures. In summary, the overall contribution of the study is categorized into two: (1) sufficient conditions which ensure the global asymptotic and exponential stability are derived in a novel manner; (2) an image encryption algorithm is proposed by considering the FOFCNN as pseudo-random number generator (PRNG), which outperforms the existing encryption algorithms. © 2019