摘要：In this paper, the author puts forward a kind of anti-periodic boundary value problems of fractional equations with the Riemann-Liouville fractional derivative. More precisely, the author is concerned with the following fractional equation: D 0 + α u ( t ) = f ( t , u ( t ) , u ′ ( t ) ) , t ∈ ( 0 , 1 ) with the anti-periodic boundary value conditions t 2 − α u ( t ) t → 0 + = − t 2 − α u ( t ) t = 1 , ( t 2 − α u ( t ) ) t → 0 + ′ = − ( t 2 − α u ( t ) ) t = 1 ′ , where D 0 + α denotes the standard Riemann-Liouville fractional derivative of order α ∈ ( 1 , 2 ) , and the nonlinear function f ( t , ⋅ , ⋅ ) may be singular at t = 0 . By applying the contraction mapping principle and the other fixed point theorem, the author obtains the existence and uniqueness of solutions. MSC:34A08, 34B15.
关键词：fractional differential equations ; anti-periodic boundary value problems ; existence results ; fixed point theorem
