非线性中立型分数阶微分方程解的存在性

Existence Conditions of Solutions for a Class of Neutral Fractional Nonlinear Ordinary Differential Equations

本文讨论了一类中立型分数阶常微分方程初值问题解的存在性。基于Picard逐次逼近方法建立函数列,然后利用不等式的缩放判定该函数列的敛散性,最终获得此类微分方程解的存在性条件。该结果是整数阶常微分方程的推广,并给出一个相应的例子来说明所得结果的有效性和适用性。

In this paper, we discuss the existence of the solutions to initial value problems for a class of neutral fractional ordinary differential equations. Based on Picard’s successive approximation method, the function sequence is established, and then the convergence and divergence of the function sequence are determined by the scaling of inequality. Finally, the existence conditions of the solutions of this kind of differential equations are obtained. The results are the generalization of integer order differential equations, and a corresponding example is given to illustrate the validity and applicability of the obtained results.