Fox-Function Representation of a Generalized Arrhenius Law and Applications

Summary

In this contribution we will present a FOX H-FUNCTION formulation of a generalized exponential function (Arrhenius Law), which describes the central concept of anomalous particle transport including anomalous relaxation / diffusion processes, in disordered but scaling materials. We will develop a fractional concept for the mathematical description of anomalous relaxation processes based on linear fractional differential equations of type d^α/dt^α where, 0 < α < 1, α is the order of fractional differentiation (α ≠ 1): We also will present a transformation procedure for semi-fractional (α = 1/2, 3/2,...) linear differential equations to a system of integer number ordinary differential equations. This last formulation of the relaxation problem takes the term “fractals” out of the picture. As examples we compare our theoretical results on mechanical stress relaxation of a plastic material, and to the rebinding process of CO to myoglobin (Mb) after photodissociation for a test of the generalized Arrhenius Law.