Solvability of Some Two-Point Fractional Boundary Value Problems under Barrier Strip Conditions

Abstract

Topological techniques are used to establish existence results for a class of fractional differential equations Dαx(t)=f(t,x(t),Dα-1x(t)), with one of the following boundary value conditions: x(0)=A and Dα-1x(1)=B or Dα-1x(0)=A and x(1)=B, where 1<α≤2 is a real number, Dαx(t) is the conformable fractional derivative, and f:[0,1]×R2→R is continuous. The main conditions on the nonlinear term f are sign conditions (i.e., the barrier strip conditions). The topological arguments are based on the topological transversality theorem.