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^αx(t) = f(t, x(t), D^α−1 x(t)), x(0) = A, x(1) = B, where 1 α ≤ 2, D^αx(t) is the conformable fractional derivative, and f : [0, 1] × R² → R is a continuous function. The main condition is sign condition. The method used is based upon the theory of fixed-point index.