Caputo分数阶微分方程初值问题解的存在性与惟一性

J4 ›› 2013, Vol. 48 ›› Issue (4): 60-64.

Caputo分数阶微分方程初值问题解的存在性与惟一性

李娇

天津大学理学院, 天津 300072

收稿日期:2012-09-04 出版日期:2013-04-20 发布日期:2013-04-16
作者简介:李娇(1986- ), 女,硕士研究生,研究方向为微分算子谱理论. Email:jiaolitju@163.comCaputo

Existence and uniqueness results for Caputo fractional differential equations with initial value conditions

LI Jiao

School of Science, Tianjin University, Tianjin 300072, China

Received:2012-09-04 Online:2013-04-20 Published:2013-04-16

摘要/Abstract

摘要：

研究了Caputo分数阶微分方程Dn*0y(x)=f(x,y(x))的初值问题,其中微分方程的阶数n∈(0,1),函数f(x,y(x))满足一定的可积条件,在相对较弱的条件下利用皮卡逐步逼近法证明了解的存在性与惟一性。最后给出一个例子说明了结果的可行性。

关键词: Caputo分数阶微分算子;初值问题;存在性;惟一性;Picard逐步逼近法

Abstract:

The Caputo fractional differential equations Dn*0y(x)=f(x,y(x)) with initial value conditions are investigated, where n∈(0,1) and the function f(x,y(x)) meets some integrable conditions. Existence and uniqueness results of solutions are obtained by the method of successive approximations under some weak conditions. An example is given to illustrate the results at last.

Key words: Caputo fractional differential operators; initial value problems; existence; uniqueness; Picard successive approximations

李娇. Caputo分数阶微分方程初值问题解的存在性与惟一性[J]. J4, 2013, 48(4): 60-64.

LI Jiao. Existence and uniqueness results for Caputo fractional differential equations with initial value conditions[J]. J4, 2013, 48(4): 60-64.

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