Article ID Journal Published Year Pages File Type
840964 Nonlinear Analysis: Theory, Methods & Applications 2011 12 Pages PDF
Abstract

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 D0+αx(t)=f(t,x),t∈(0,+∞),0<α≤1, where D0+α is the standard Riemann–Liouville fractional derivative, subject to the initial value condition limt→0+t1−αx(t)=u0. 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,+∞)[0,+∞). Moreover, in the case α=1α=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.

► We study the IVPs for nonlinear fractional differential equations. ► We construct a special Banach space. ► Some global existence results of solutions on the half-axis are obtained. ► Existence results of solutions of IVPs for ODEs on the half-axis are also included.

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Physical Sciences and Engineering Engineering Engineering (General)
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