Fractional dynamics has experienced a firm upswing during the past few years, having been
forged into a mature framework in the theory of stochastic processes. A large number of …

Fractal structures are found everywhere in nature, and as a consequence anomalous
diffusion has far reaching implications in a host of phenomena. This book describes diffusion …

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian
process in a fractional dimensional space with a suitable metric. This allows us to define the …

We investigate a generalized Langevin equation (GLE) in the presence of an additive noise
characterized by the mixture of the usual white noise and an arbitrary one. This scenario …

We analyze random walk through fractal environments, embedded in three-dimensional,
permeable space. Particles travel freely and are scattered off into random directions when …

In this Letter, we develop an analytical approach which provides an explicit determination of
mean first-passage times (MFPTs) for random walks in bounded domains for a wide class of …

We consider a Markovian jum** process which is defined in terms of the jump-size
distribution and the waiting-time distribution with a position-dependent frequency, in the …

We consider a mortal random walker on a family of hierarchical graphs in the presence of
some trap sites. The configuration comprising the graph, the starting point of the walk, and …

We point out that the chemical space of a totally disconnected Cantor dust K n⊂ E n is a
compact metric space C n with the spectral dimension ds= d ℓ= n> D, where D and d ℓ= n …

A number of distinct differential equations, known as generalized diffusion equations, have
been proposed to describe the phenomenon of anomalous diffusion on fractal objects …