Fractional Calculus: Application and Results

Over the last two decades, anomalous relaxation and diffusion processes have been studied from both the experimental and theoretical point of view. Anomalous transport processes occur usually in so-called complex (that is, disordered) systems. Here, we review some recent developments in modeling non-standard relaxation and diffusion equations based on Riemann-Liouville fractional calculus techniques. Closed analytical expressions of the solutions of such fractional differential equations are given in terms of Fox's H-functions. The analytical calculations carried out are fully supported by our Mathematica package FractionalCalculus.