On piecewise continuous solutions of higher order impulsive fractional differential equations and applications

被引：19
|
作者：
Liu, Yuji [1 ]
机构：
[1] Guangdong Univ Finance & Econ, Dept Math, Guangzhou 510000, Guangdong, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 287卷
关键词：
Higher order fractional differential equation; Piecewise continuous solution; Impulse effect; Caputo derivative; Riemann-Liouville derivative; EXISTENCE;
D O I：
10.1016/j.amc.2016.03.041
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For impulsive differential equations with fractional order, we show that the formula of solutions in cited papers are incorrect. We then give exact piecewise continuous solutions (the explicit solutions) of two classes of fractional differential equations of order alpha is an element of (n = 1, n) involving Caputo derivatives and Riemann-Liouville derivatives. Apply our results to obtain existence of solutions of two classes of initial value problems of singular impulsive fractional differential equations. Examples are presented to illustrate the main theorems. (C) 2016 Published by Elsevier Inc.
引用
收藏
页码：38 / 49
页数：12
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