A numerical method for solving a class of nonlinear second order fractional volterra integro-differntial type of singularly perturbed problems

In this paper, we study a class of fractional nonlinear second order Volterra integro-differential type of singularly perturbed problems with fractional order. We divide the problem into two subproblems. The first subproblems is the reduced problem when ε = 0. The second subproblems is fractional Volterra integro-differential problem. We use the finite difference method to solve the first problem and the reproducing kernel method to solve the second problem. In addition, we use the pade' approximation. The results show that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. Theoretical results are presented. Numerical results are presented to show the efficiency of the proposed method.