<p>Nonlinearity appears everywhere around us from natural events like weather, climate to various human activities like global warming. Nonlinear systems exhibit complex, rich and even chaotic responses for a rather simpler inputs. This complexity proves crucial in modelling of the biological, chemical, physical model in a realistic manner. In the field of electronics, nonlinear circuits are crucial in development of technologies like sensors, neuromorphic systems and so on. Understanding the nonlinear characteristics is vital in constructing the models that mimics the nature itself. The mem-elements in simple terms can be considered as nonlinear circuit components that depends on their past. The review article focuses on the application to fractional order mem-elements and their role in enhancing the neural network architecture. An analysis of multidisciplinary research by employing fractional calculus, computational simulations, hardware design, and encryption applications was conducted. Significant findings suggest that fractional-order models improve neural network representation better than the integer-order systems by capturing complex memory impacts and dynamic phenomena like chaos and multi-stability. This comprehensive review of the literature and the future trends will offer necessary insights to the researchers who seek to develop novel theory and practical applications of the fractional order derivative systems in the field of electronics and neurosciences.</p>