Iterative approximation of solutions for nonlinear fractional differential equations with non-separated integral boundary conditions

Abstract

In this paper, the monotone iterative method combined with spectral theory is applied to obtain approximate analytical solutions of nonlinear fractional differential equations with deviating arguments. This approach provides constructive proof of existence as well as numerical procedures for computation of solutions. A numerical iterative scheme is introduced to obtain an accurate approximate solution for the problem under the assumption of existing only a lower solution (or an upper solution). Finally, an example illustrating how the theory can be applied in practice is also included.