Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation

This paper considers a class of boundary value problemsfor the semilinear singularly perturbed fractional differentialequation. Under the suitable conditions, firstly, the outer solutionof the original problem is obtained; secondly, using the stretchedvariable and the composing expansion method the boundary layer isconstructed; finally, using the theory of differential inequalitiesthe asymptotic behaviour of solution for the problem is studied andthe uniformly valid asymptotic estimation is discussed.