相关论文: Favard separation method for almost periodic stoch…
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…
In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of…
In this paper, an analytic approximation method for highly nonlinear equations, namely the homotopy analysis method (HAM), is employed to solve some backward stochastic differential equations (BSDEs) and forward-backward stochastic…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…
This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The…
The known Levitan's Theorem states that the linear differential equation $$ x'=A(t)x+f(t) \ \ \ (*) $$ with Bohr almost periodic coefficients $A(t)$ and $f(t)$ admits at least one Levitan almost periodic solution if it has a bounded…
This paper presents a novel semi-analytical collocation method to solve multi-term variable-order time fractional partial differential equations (VOTFPDEs). In the proposed method it employs the Fourier series expansion for spatial…
The technique of stochastic solutions, previously used for deterministic equations, is here proposed as a solution method for partial differential equations driven by distribution-valued noises.
This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to…
A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We examine such structured problems which also depend on a parameter vector and study the problem of…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
This note contains a short and simple proof of Wormald's differential equation method (that yields slightly improved approximation guarantees and error probabilities). This powerful method uses differential equations to approximate the…
As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly employed in the related…
It is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear abstract functional differential equations in both, the finite and infinite delay case. A generalization of the integral…
Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Pad\'e approximants for solving nonlinear partial differential equations…
We present a novel solution method for It\^o stochastic differential equations (SDEs). We subdivide the time interval into sub-intervals, then we use the quadratic polynomials for the approximation between two successive intervals. The main…
The paper describes different approaches to generalize the trapezoidal method to fractional differential equations. We analyze the main theoretical properties and we discuss computational aspects to implement efficient algorithms. Numerical…
This paper establishes the averaging method to a coupled system consisting of two stochastic differential equations which has a slow component driven by fractional Brownian motion (FBM) with less regularity $1/3< H \leq 1/2$ and a fast…
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion…