Some linear fractional stochastic equations

Some linear fractional stochastic equations

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases. When the drift is zero, we show that in the one-parameter case the solution in an exponential, thus positive, function while in the two-parameter settings t...

Remarks on some linear fractional stochastic equations

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases. When the drift is zero, we show that in the one-parameter case the solution in an exponential, thus positive, function while in the two-parameter settings t...

Asymptotically Linear Solutions for Some Linear Fractional Differential Equations

and Applied Analysis 3 The first variant of differential operator was used in 13 to study the existence of solutions x t of nonlinear fractional differential equations that obey the restrictions x t −→ 1 when t −→ ∞, x′ ∈ ( L1 ∩ L∞ ) 0, ∞ ,R . 1.5 The second variant of differential operator, see 14 , was employed to prove that, for any real numbers x0, x1, the linear fractional differential equ...

On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space

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.