Comparison principles for fractional differential equations with the Caputo derivatives

被引：0
作者：
Ziqiang Lu
Yuanguo Zhu
机构：
[1] Nanjing University of Science and Technology,School of Science
来源：
Advances in Difference Equations | / 2018卷
关键词：
Comparison principle; Fractional differential equation; Caputo derivatives; Local existence; Extremal solutions; 26A33; 26D10; 34A12; 34A40;
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摘要：
In this paper, we deal with comparison principles for fractional differential equations involving the Caputo derivatives of order p with 0≤n−1<p≤n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$0\leq n-1< p\leq n$\end{document}. First, we present comparison results with strict inequalities for fractional differential equations with the Caputo derivatives. Then we investigate local existence and extremal solutions for fractional differential equations with the Caputo derivatives. Finally, we consider comparison results with nonstrict inequalities for fractional differential equations with the Caputo derivatives.
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