On the Integration of Fractional Neuronal Dynamics Driven by Correlated Processes

The stochastic Leaky Integrate-and-Fire (LIF) model is revisited adopting a fractional derivative instead of the classical one and a correlated input in place of the usual white noise. The aim is to include in the neuronal model some physiological evidences such as correlated inputs, codified input currents and different time-scales. Fractional integrals of Gauss-Markov processes are considered to investigate the proposed model. Two specific examples are given. Simulations of paths and histograms of first passage times are provided for a specific case.