Fractional Dynamics: A Statistical Perspective

Abstract

Fractional calculus is a mathematical paradigm that has been increasingly adopted to describe the dynamics of systems with hereditary characteristics, or that reflect an average of a large population of micro elements. In this line of thought, this article analyzed the statistical dynamics of a system composed of a large number of micro-mechanical masses with backlash and impacts. We conclude that, while individual dynamics of each element has an integer order nature, the global dynamics reveal the existence of both integer and fractional dynamics.