Solvability of Some Two-Point Fractional Boundary Value Problems under Barrier Strip Conditions. (26th October 2017)

• Record Type: Journal Article
• Authors: He, Limei; Dong, Xiaoyu; Bai, Zhanbing; Chen, Bo
• Other Names: De la Sen Manuel Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2017(2017)
• Publication Date: 2017-10-26
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2017/1465623
• Languages: English
• ISSNs: 2314-8896

Abstract

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.