In this paper we discuss stochastic di erential delay equations with Markovian switching. Such an equation can be regarded 9 as the result of several stochastic di erential delay equations switching from one to another according to the movement of a Markov chain. The aim of this paper is to investigate the stability in distribution of the equations. 11 c © 2003 Published by Elsevier Science B.V.

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population of discrete individuals characterized by one or several adaptive traits. The population is modelled as a stochastic point process whose generator captures t...

An approach for transforming systems of partial di erential equations in order to obtain new formulations which are more accessible to numerical solution is studied. An algorithm is developed for generating such transformations automatically, using symbolic computations employing Gr obner bases. The algorithm is implemented using freely available software. This approach, along with planned dev...

We de ne a discrete (integer-valued) Lyapunov function V for cyclic nearest neighbor systems of di erential delay equations possessing a feedback condition. This extends analogous de nitions for cyclic systems of ODE's, and for scalar di erential delay equations. We relate the values of V to the real parts of the Floquet multipliers for such linear periodic systems, and thereby prove all Floque...

Einstein's eld equations for spatially self-similar locally rotationally symmetric perfect uid models are investigated. The eld equations are rewritten as a rst order system of autonomous ordinary di erential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system of di erential equations is reduced as far as possible. The system is subsequ...

a novel and eective method based on haar wavelets and block pulse functions(bpfs) is proposed to solve nonlinear fredholm integro-dierential equations of fractional order.the operational matrix of haar wavelets via bpfs is derived and together with haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. our new m...

in this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. utilizing the generalized characterization theorem. then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. here neural network is considered as a part of large eld called n...

1. Introdu tion. There are plenty of appli ation papers in whi h kernels or radial basis fun tions are su essfully used for solving partial di erential equations by meshless methods. The usage of kernels is typi ally based on spatial interpolation at s attered lo ations, writing the trial fun tions entirely in terms of nodes [2℄. For stationary partial di erential equations, the dis retization ...

We classify all partial di¤erential equations with polynomial coe¢ cients in x and y of the form A(x)uxx + 2B(x; y)uxy + C(y)uyy +D(x)ux + E(y)uy = nu; which has weak orthogonal polynomials as solutions and show that partial derivatives of all order are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial di¤erential equations in d-variables.