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.
- Caputo fractional derivative
- Nonlinear boundary value problem
- Singularly perturbed volterra integro-differntial
ASJC Scopus subject areas
- General Mathematics