Uniform asymptotic stability of solutions of fractional functional differential equations

In this paper, some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worthy mentioning that when $\alpha=1$ the initial value problem (1.1) reduces to a classical dissipative differential equation with delays in [4]Comment: 18 pages, 2 figure

Global existence and stability for second order functional evolution equations with infinite delay

In this article, the authors give sufficient conditions for existence and attractivity of mild solutions for second order semi-linear functional evolution equation in Banach spaces using Schauder's fixed point theorem. An example is provided to illustrate the result

Impulsive neutral functional differential equations driven by a fractional Brownian motion with unbounded delay

In this paper, we prove the local and global existence and attractivity of mild solutions for stochastic impulsive neutral functional differential equations with infinite delay, driven by fractional Brownian motion.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadJunta de Andalucí

Monotonicity and asymptotic behavior of solutions for Riemann-Liouville fractional differential equation

In this paper, we first investigate the monotonicity and limit problem of the fractional integral functions. By fixed point theorem and these new results of the fractional integral functions, we present that the Riemann-Liouville fractional differential equations has at least one decreasing solution in $C_{1-\beta}^{+}(0,+\infty)$. The asymptotic behavior of solutions is also discussed under some different conditions. The novelty in this paper is that we investigate the asymptotic behavior of Riemann-Liouville fractional differential equations by the monotonicity of functions. Finally, several examples are given to illustrate our main results