Explicit iteration to a nonlinear fractional Langevin equation with non-separated integro-differential strip-multi-point boundary conditions

Abstract

By using the monotone iterative method combined with the upper and lower solutions, we not only prove the existence of extremal solutions for the nonlinear fractional Langevin equation involving fractional conformable derivative and non-separated integro-differential strip-multi-point boundary conditions, but also provide two computable explicit monotone iterative sequences that converge to the extremal solution. In order to carry out our work smoothly, we also develop a comparison principle, which plays a very important role in this article. (C) 2019 Elsevier Ltd. All rights reserved.