Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

The convergence of discrete approximations of generalized reflected backward stochastic differential equations with random terminal time in a general convex domain is studied. Applications to investigation obstacle elliptic problem with Neumann boundary condition for partial differential equations are given.

in this paper, we investigate some problems which can be reduced to the goursat problem for afourth order equation. some results and theorems are given concerning the existence and uniqence for thesolution of the suggested problem.

A numerical approach for the approximation of inertial manifolds of stochastic evolutionary equations with multiplicative noise is presented and illustrated. After splitting the stochastic evolutionary equations into a backward and a forward part, a numerical scheme is devised for solving this backward-forward stochastic system, and an ensemble of graphs representing the inertial manifold is co...

In this paper we introduce a new kind of Backward Stochastic Differential Equations, called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness and regularity of solution to ergodic BSDEs. Then we apply these results to the optimal ergodic control of a Banach valued stochastic state equation. We also establish the link between the erg...

this paper presents a new numerical method for solution of eikonal equation in two dimensions.in contrast to the previously developed methods which try to define the solution surface by its level sets(contour curves), the developed methodology identifies the solution surface by resorting to its characteristics. the suggested procedure is based on the geometric properties of the solution surface...

this paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...

We explore Itô stochastic differential equations where the drift term has possibly infinite dependence on the past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proved if the dependence on the past decays sufficiently fast. The results of this paper ar...

The purpose of this article is to giye an overview of some recent developments in optimal stochastic control theory. The field has expanded a great deal during the last 20 years. It is not possible in this overview to go deeply into any topic, and a number of interesting topics have been omitted entirely. The list of references includes several books, conference proceedings and survey articles....

In this paper, we initiate a study on optimal control problem for stochastic differential games under generalized expectation via backward stochastic differential equations and partial information. We first prove a sufficient maximum principle for zero-sum stochastic differential game problem. And then extend our approach to general stochastic differential games (nonzero–sum games), and obtain ...