Multi-point boundary value problems for a class of Riemann-Liouville fractional differential equations

Abstract

Abstract In this paper, we shall study the existence and uniqueness of solutions for the multi-point boundary value problem of fractional differential equations D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , 2 < α ≤ 3 , with boundary conditions u ( 0 ) = 0 , D 0 + β u ( 0 ) = 0 , D 0 + β u ( 1 ) = ∑ i = 1 m − 2 b i D 0 + β u ( ξ i ) , 1 ≤ β ≤ 2 , involving Riemann-Liouville fractional derivatives D 0 + α and D 0 + β . We use the nonlinear alternative of Leray-Schauder and the Banach contraction mapping principle to obtain the existence and uniqueness of solutions. Some examples are given to show the applicability of our main results. MSC:34A08, 34K10.