Shock wave solution for a class of nonlinear nonlocal singularly perturbed fractional differential equation |
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| Authors: | Juanrong Shi Jiaqi Mo |
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| Institution: | 1.Department of Basic Teaching,Anhui Technical College of Mechanical and Electrical Engineering,Anhui,China;2.Department of Mathematics,Shanghai Jiaotong University,Shanghai,China;3.Department of Mathematics,Anhui Normal University,Anhui,China |
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| Abstract: | 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. |
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