Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis

The main aim of this paper is to study the global existence of solutions of initial value problems for nonlinear fractional differential equations(FDEs) on the half-axis, which is fundamental in the basic theory of FDEs and important in stability analysis of this kind of equations. In this paper, we are concerned with the nonlinear FDE D(0+)(alpha)x( t) = f ( t, x), t is an element of ( 0,+infinity), 0 < alpha <= 1, By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained to guarantee the global existence of solutions on the interval [0,+infinity). Moreover, in the case alpha = 1, existence results of solutions of initial value problems for ordinary differential equations on the half-axis are also obtained. An interesting example is also included. (C) 2011 Elsevier Ltd. All rights reserved.