Abstract: A class of Cauchy problem for the nonlinear nonlocal singular perturbation fractional order equation was considered. First, the outer solution to the original Cauchy problem was obtained. Then, using the stretched variables and the composing expansion method the shock wave layer and initial layer were constructed. Finally, using the theory of differential inequality the asymptotic behavior of the solution to the original Cauchy problem of nonlinear nonlocal singular perturbation fractional order equation was studied and its uniformly valid asymptotic estimation was proved.

Key words: nonlinear, fractional order differential equation, shock wave