Fractional Calculus: Application and Results

Gerd Baumann
Department of Mathematical Physics, University of Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany

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, i.e. in 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.