This work is devoted to investigating exact solutions of generalized nonlinear fractional diffusion equations with external force and absorption. We first investigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones. In both situations, we...

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(Sα(t)), 0α1, here dX(τ)=μX(τ)(dτ)2H+σX(τ)dBH(τ), as a model of asset prices, which captures the subdiffusive...

It is proved that the asymptotic shape of the solution for a wide class of fractional Fokker–Planck-type equations with coefficients depending on coordinate and time is a stretched Gaussian for the initial condition being pulse function in the homogeneous and heterogeneous fractal structures,...

In this paper, we study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with memory. In our models, the waiting time involves Riemann–Liouville fractional derivative or Riemann–Liouville fractional integral....

In this paper, in order to establish connection between fractional derivative and fractional Brownian motion (FBM), we first prove the validity of the fractional Taylor formula proposed by Guy Jumarie. Then, by using the properties of this Taylor formula, we derive a fractional Itô formula for...

In this paper, a generalized diffusion model driven by the composite-subdiffusive fractional Brownian motion (FBM) is employed. Based on this stochastic process, we derive a fractional Fokker–Planck equation (FFPE) and obtain its solution. It is proved that the Generalized Einstein Relation...

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with diffusion coefficient separable in time and space, D(t,x)=D(t)|x|−θ, subject to absorbing boundary condition and the conventional initial...

When memory sets are random variation sets of the self-similar set and the total number of remaining states in each stage of the division of this set is normalized to unity, the corresponding flux and fractional integral are “robust” and stable under some conditions. This answers an open...

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with a space- and time-dependent diffusion coefficient subject to absorbing boundaries and the initial condition. We obtain explicit analytical...

This paper studies the Hausdorff dimensions of random non-self-similar fractals. Here, we obtain the Hausdorff dimensional estimates of random net fractals generated by random contractions (including random transformation contraction and random ratio contraction). In addition, we give the...