Uniform Asymptotic Stability Of Solutions Of Fractional Functional Differential Equations

A fractional differential equation is an equation which contains fraction-al derivatives; a fractional integral equation is an integral equation containing fractional integrals. A fractional-order system means a system described by a fractional differential equation or a fractional integral equation or by a system of such equations. It is well known that there is a very wide range of applications of fractional differential equations, especially in physics. However, there is little reference on the uniform asymptotic stability of fractional substantial functional differential equations, even, in the case of without delays.In this paper, we are interested in the uniform asymptotic stability of frac-tional substantial functional differential equations, and the global existence and uniform asymptotic stability results are proved under the assumption that the nonlinear term f(t, yt) satisfies two kinds of conditions. In particular, it is worthy mentioning that when α=1the initial value problem reduces to a classical dissipative functional differential equation with delays in [1].