Stability of Equilibrium Points of Differential Equation with Fractional Nonlinearity and Stochastic Perturbations

Stability of Equilibrium Points of Fractional Difference Equations with Stochastic Perturbations

Recommended by Jianshe Yu It is supposed that the fractional difference equation xn 1 μ ∑k j 0ajxn−j / λ ∑k j 0bjxn−j , n 0, 1, . . . , has an equilibrium point x̂ and is exposed to additive stochastic perturbations type of σ xn − x̂ ξn 1 that are directly proportional to the deviation of the system state xn from the equilibrium point x̂. It is shown that known results in the theory of stability o...

Stability of Small Periodic Waves in Fractional KdV-Type Equations

We consider the effects of varying dispersion and nonlinearity on the stability of periodic traveling wave solutions of nonlinear PDEs of KdV type, including generalized KdV and Benjamin–Ono equations. In this investigation, we consider the spectral stability of such solutions that arise as small perturbations of an equilibrium state. A key feature of our analysis is the development of a nonloc...

Mittag-Leffler-Hyers-Ulam Stability of Fractional Differential Equation

In this article, we study the Mittag-Leffler-Hyers-Ulam and Mittag-Leffler-Hyers-Ulam-Rassias stability of a class of fractional differential equation with boundary condition.

Stochastic differential inclusions of semimonotone type in Hilbert spaces

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...

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