Shock wave solution for a class of nonlinear nonlocal singularly perturbed fractional differential equation

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• 作者：Juanrong Shi ; Jiaqi Mo
• 关键词：nonlinear ; fractional differential equation ; shock wave
• 刊名：Wuhan University Journal of Natural Sciences
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：22
• 期：1
• 页码：13-18
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Life Sciences, general; Materials Science, general; Computer Science, general;
• 出版者：Wuhan University
• ISSN：1993-4998
• 卷排序：22

文摘

A class of boundary value problems for the nonlinear nonlocal singularly perturbed fractional differential equation is considered. Firstly, the outer solution of the original problem is obtained. Secondly, by using the stretched variables and the composing expansion method, the shock wave layer and boundary layers are constructed. Finally, by using the theory of differential inequality, the asymptotic behavior of solution for the original boundary value problem of nonlinear nonlocal singularly perturbed fractional differential equation is studied. And the uniformly valid asymptotic estimation is discussed.