Some linear fractional stochastic equations

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Solutions for some non-linear fractional differential equations with boundary value problems

In recent years, X.J.Xu [1] has been proved some results on mixed monotone operators.  Following the paper of X.J.Xu, we study the existence and uniqueness of the positive solutions for non-linear differential equations with boundary value problems. 

Semilinear Stochastic Equations in a Hilbert Space with a Fractional Brownian Motion

The solutions of a family of semilinear stochastic equations in a Hilbert space with a fractional Brownian motion are investigated. The nonlinear term in these equations has primarily only a growth condition assumption. An arbitrary member of the family of fractional Brownian motions can be used in these equations. Existence and uniqueness for both weak and mild solutions are obtained for some ...

Computational Method for Fractional-Order Stochastic Delay Differential Equations

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

Basic results on distributed order fractional hybrid differential equations with linear perturbations

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

Self-Similar Processes, Fractional Brownian Motion and Statistical Inference

Self-similar stochastic processes are used for stochastic modeling whenever it is expected that long range dependence may be present in the phenomenon under consideration. After discusing some basic concepts of self-similar processes and fractional Brownian motion, we review some recent work on parametric and nonparametric inference for estimation of parameters for linear systems of stochastic ...