The rapid expansion of artificial intelligence (AI) technologies necessitates the resolution of data handling and storage limitations inherent in the von Neumann computer architecture. Drawing inspiration from biology, which initially sparked the development of artificial neural networks, we explore a new avenue in computer architecture known as neuromorphic computing. Based on the emergence of iontronic fluidic ionic/electronic components, here we show the application of a nanopore ionic rectifier as a synapse element that exhibits conductance modulation in response to a train of voltage impulses, producing programmable resistive states. The memristive properties and their connection to hysteresis phenomena are elucidated by the combined analysis in time and frequency domains. Notably, our findings underscore the prevalence of an inductor mechanism, which arises from the interplay between fast and slow conduction modes. The activation time of this mechanism governs the biomimetic attributes of synaptic conductance potentiation, depression, and paired pulse facilitation. This innovative approach enables the creation of high-fidelity memory elements reminiscent of biological systems and holds promise for significantly enhancing the efficiency and sustainability of AI systems.