The fractional diffusion equation is derived from the master equation of continuous time random walks (CTRWs) via a straightforward application of the GnedenkoKolmogorov limit theorem. The Cauchy problem for the fractional diffusion equation is solved in various important and general cases. The meaning of the proper diffusion limit for CTRWs is discussed.

Solitary fibrous tumors are unusual neoplasms that are rarely found in the liver parenchyma. Th ey are usually described as hard, grayish white, well-defined lesions. Predominant cystic change in a solitary fibrous tumor is an unexpected finding, with only a few previous cases reported in the literature, two of which are localized in the head and neck region. Herein, we report a unique case of ...

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result,...

| We consider di erential equations A(x) _ x = g(x), where A is an n n-matrix of C 1 functions and g is C 1 . We investigate the above di erential equation about singular points x 0 that are standard in the sense of Rabier. In particular, the null space of A(x 0 ) is of dimension 1. We show that there is a C 1 -di eomorphism that transforms the above equation about x 0 into x 1 _ x 1 = 1, _ x 2...

We present a method to solve initial and boundary value problems using arti ial neural networks. A trial solution of the di erential equation is written as a sum of two parts. The rst part satis es the initial/boundary onditions and ontains no adjustable parameters. The se ond part is onstru ted so as not to a e t the initial/boundary onditions. This part involves a feedforward neural network, ...

in this paper, the dierential transform method (dtm) is applied to the fisherequation. this method can be used to obtain the exact solutions of fisherequation. finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. these resultsshow that this technique is easy to apply.

Hybrid action systems extend a conventional action system with a guarded di erential equation | a di erential action | that de nes evolution of continuous variables while the guard remains true. The new action is given a weakest liberal precondition semantics, which is illustrated by examples from a train model. The example motivates a discussion of priorities in a system of iterated di erentia...

We consider the fractional generalizations of equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with noninteger mass dimensions. Using fractional integrals, we derive the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski equation). In this paper fractional Fokker-Planck equation for fractal media is derived f...

the aim of this paper is to present a new numerical method for solving the bagley-torvik equation. this equation has an important role in fractional calculus. the fractional derivatives are described based on the caputo sense. some properties of the sinc functions required for our subsequentdevelopment are given and are utilized to reduce the computation of solution of the bagley-torvik equatio...