Shock Wave Solution for a Class of Nonlinear Nonlocal Singularly Perturbed Fractional Differential Equation  

作　　者：SHI Juanrong MO Jiaqi 

机构地区：[1]Department of Basic Teaching,Anhui Technical College of Mechanical and Electrical Engineering [2]Department of Mathematics,Shanghai Jiaotong University [3]Department of Mathematics,Anhui Normal University

出　　处：《Wuhan University Journal of Natural Sciences》2017年第1期13-18,共6页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China(40676016);the Natural Science Foundation of the Education Department of Anhui Province(KJ2015A418)

摘　　要：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.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.

关 键 词：NONLINEAR fractional differential equation SHOCKWAVE 

分 类 号：O175.14[理学—数学]