Existence results for the fractional differential equations with multi-strip integral boundary conditions

Abstract

In this paper, we consider the existence of solutions for the fractional differential equations with multi-point and multi-strip boundary conditions. The existence results are obtained by applying Leray–Schauder’s alternative, while the uniqueness of solution is established via Banach’s contraction principle. We also consider the existence of positive solutions for the fractional differential equations with degenerated multi-strip integral boundary conditions. We come to the results by applying the Krasnoselskii’s fixed point theorem. Some examples are also presented to illustrate the main results.