In this article, the authors discuss a dynamic procedure that makes fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. The authors find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent...

In this article, the authors study a fully connected network (cluster) of interacting two-state units as a model of cooperative decision making. Each unit in isolation generates a Poisson process with rate g. The authors show that when the number of nodes is finite, the decision-making process...

The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional...

A computational model for the distribution of wealth among the members of an ideal society is presented. It is determined that a realistic distribution of wealth depends upon two mechanisms: an asymmetric flux of wealth in trading transactions that advantages the poorer of the two traders and a...

Exact first and second order statistics of a damped mechanical oscillator with a fluctuating frequency and driven by a fluctuating force are obtained. All the cumulants of the fluctuating frequency are assumed to be delta correlated, while those of the driving force are of arbitrary form. The...

Econophysics provides a strategy for understanding the potential mechanisms underlying the anomalous distribution of wealth found in real societies. We present a computational nonlinear stochastic model for the distribution of wealth that depends upon three parameters and two mechanisms: trade...

The distribution of wealth among the members of a society is herein assumed to result from two fundamental mechanisms, trade and investment. An empirical distribution of wealth shows an abrupt change between the low-medium range, that may be fitted by a non-monotonic function with an...

We study the response to perturbation of non-Poisson dichotomous fluctuations that generate super-diffusion. We adopt the Liouville perspective and with it a quantum-like approach based on splitting the density distribution into a symmetric and an anti-symmetric component. To accomodate the...