Solvability of Some Two-Point Fractional Boundary Value Problems under Barrier Strip Conditions. (26th October 2017) - He, Limei; Dong, Xiaoyu; Bai, Zhanbing; Chen, Bo
Abstract : Topological techniques are used to establish existence results for a class of fractional differential equations D α x ( t ) = f ( t, x ( t ), D α - 1 x ( t ) ), with one of the following boundary value conditions: x ( 0 ) = A and D α - 1 x ( 1 ) = B or D α - 1 x ( 0 ) = A and x ( 1 ) = B, where 1 < α ≤ 2 is a real number, D α x ( t ) is the conformable fractional derivative, and f : [ 0, 1 ] × R 2 → 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.