Study of a nonlinear fractional boundary value problem via the dichotomy-type technique

We present a new view onto the successive approximations’ approach in study of the two-point nonlinear fractional boundary value problems. In order to reduce the original problem and further construct its approximate solution we use the co-called ‘freezing’ technique and the dichotomy-type approach. These lead to improvement of the sufficient conditions for application of the aforementioned method and sharpen the obtained estimates.