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

作　　者：勾明志 付洋 蔡克珍 GOU Mingzhi;FU Yang;CAI Kezhen(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2020年第2期18-22,共5页Journal of Anqing Normal University(Natural Science Edition)

摘　　要：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.

关 键 词：中立型分数阶微分方程 分数阶导数 分数阶积分 Picard逐次逼近 

分 类 号：O175.1[理学—数学]