XU Jianzhong, MO Jiaqi. Asymptotic Solution for Fractional-Order 2-Parameter High-Order Nonlinear Perturbed Models[J]. Applied Mathematics and Mechanics, 2020, 41(6): 679-686. doi: 10.21656/1000-0887.400238
Citation: XU Jianzhong, MO Jiaqi. Asymptotic Solution for Fractional-Order 2-Parameter High-Order Nonlinear Perturbed Models[J]. Applied Mathematics and Mechanics, 2020, 41(6): 679-686. doi: 10.21656/1000-0887.400238

Asymptotic Solution for Fractional-Order 2-Parameter High-Order Nonlinear Perturbed Models

doi: 10.21656/1000-0887.400238
Funds:  The National Natural Science Foundation of China(41275062)
  • Received Date: 2019-08-13
  • Rev Recd Date: 2019-08-27
  • Publish Date: 2020-06-01
  • A class of nonlinear fractional-order perturbed higher-order differential models was considered. Firstly, under suitable conditions, the outer solution to the original problem was obtained with the perturbation method. Then by means of the stretched variable, the composite expansion method and the theory of power series, the first and second boundary layer correction terms were constructed and the formal asymptotic expansion was obtained. Finally, with the theory of differential inequalities the asymptotic behavior of the solution to the problem was studied and the uniform validity of the asymptotic estimate expression was proved.
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