On Fractional Stochastic Modeling of Neuronal Activity Including Memory Effects

In order to model the memory and to describe the memory effects in the firing activity of a single neuron subject to a time-dependent input current, a fractional stochastic Langevin-type equation is considered. Two different discretization formulas are derived and the corresponding algorithms are implemented by means of R-codes for several values of the parameters. Reset mechanisms after successive spike times are suitably imposed to compare simulation results. The firing rates and some neuronal statistical estimates obtained by means the two algorithms are provided and discussed.