In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...

We consider the fractional generalizations of Liouville equation. The normalization condition, phase volume, and average values are generalized for fractional case. The interpretation of fractional analog of phase space as a space with fractal dimension and as a space with fractional measure are discussed. The fractional analogs of the Hamiltonian systems are considered as a special class of no...

By introducing the fractional derivatives in the sense of caputo, we use the Adomian decomposition method to construct the approximate solutions for some fractional partial differential equations with time and space fractional derivatives via the time and space fractional derivatives wave equation, the time and space fractional derivatives reduced wave equation and the (1+1)-dimensional Burger’...

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Lévy alpha -stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler...

Introduction. The mathematical theory of probability is now ordinarily formulated in terms of measure theory. The formalization of a succession of n trials is in terms of ^-dimensional measure ; that of a sequence of trials is in terms of (denumerably) infinite-dimensional measure ; that of a continuous set of trials (a set dependent on a continuous time parameter say) is in terms of measure in...

It is known that there is a only one invariant metric, and only one family of invariant affine connections on the the space of probability measures on finite sample spaces. Under certain conditions this may also true for finite measures on finite sample spaces. We extends these results to finite measures on arbitrary sample spaces. It is shown that the generalization of these structures are uni...

In this paper, Exp-function and (G′/G)expansion methods are presented to derive traveling wave solutions for a class of nonlinear space-time fractional differential equations. As a results, some new exact traveling wave solutions are obtained.

Special relativity is most naturally formulated as a theory of spacetime geometry, but within the spacetime framework probability appears to be a purely epistemic notion. It is possible that progress can be made with rather di¤erent approaches covariant stochastic equations, in particular but the results to date are not encouraging. However, it seems a non-epistemic notion of probability can be...

In this paper fractional generalization of Liouville equation is considered. We derive fractional analog of normalization condition for distribution function. Fractional generalization of the Liouville equation for dissipative and Hamiltonian systems was derived from the fractional normalization condition. This condition is considered as a normalization condition for systems in fractional phase...

We investigate a three-level system in the context of fractional Schrödinger equation by considering differential operators time and space, which promote anomalous relaxations spreading wave packet. first consider omitting kinetic term, i.e., taking into account only transition among levels, to analyze effect derivative. Afterward, we incorporate term derivative space simultaneous packet levels...