Bioelectrical memory effects behind fractional-order transients emulating synaptic plasticity in brain-inspired electrochemical dendrites

• Fractional calculus describes intrinsic memory in artificial dendrites • CPE provides a mechanistic description beyond classical fitting constructs • Cumulative Mittag-Leffler patterns capture true potentiation effects • Our theoretical model reproduces experimental transient dynamics • Dendrite-inspired circuits enable learning and temporal information processing Understanding and reproducing the brain’s ability to store and process information remains a central challenge in neuromorphic engineering. Here, we identify the physical origin and provide a phenomenological interpretation of memory effects underlying synaptic-like plasticity, realized in brain-inspired electrochemical dendrites, from fractional calculus. Using hybrid ion-electron conduction pathways, such artificial dendrites exhibit anomalous transient responses arising from the complex dynamics of ionic diffusion and electronic transport across the nanostructured interfaces, effectively embedding history-dependent behavior in the electrochemical junctions. These insights show that the constant phase element (CPE) is more than a simple fitting construct used commonly in Electrochemistry: It provides a fundamental description of multiscale transients, capturing the complex dynamical behavior associated with memory effects and their analogy to synaptic functionality. Beyond the classical Mittag-Leffler responses obtained under previous equilibrium conditions, the hereditary behavior behind artificial synaptic activity emerges as fractional-order dynamics with cumulative Mittag-Leffler patterns in the current responses, offering a natural platform for understanding device-level short- and long-term potentiation effects. Our approach, faithfully captured by a quantitative physical model validated through experiments and simulations, encodes past-state memory in neuromorphic devices, bridging physical processes and system-level modeling while enabling dendrite-inspired circuits capable of learning and temporal information processing.