Existence for fractional Dirichlet boundary value problem under barrier strip conditions

In this paper, a fixed-point theorem is used to establish existence results for fractional Dirichlet boundary value problem \[D^α x(t)=f(t,x(t),Dα-1x(t)), x(0)=A, x(1)=B\] where \(1 < α≤ 2,D^α x(t)\) is the conformable fractional derivative, and \(f : [0, 1] × R^2 → R\) is a continuous function. The main condition is sign condition. The method used is based upon the theory of fixed-point index.