Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions

Abstract

This paper studies a coupled system of nonlinear fractional differential equations with three-point boundary conditions. Applying the Schauder fixed point theorem, an existence result is proved for the following system D α u ( t ) = f ( t , v ( t ) , D p v ( t ) ) , D β v ( t ) = g ( t , u ( t ) , D q u ( t ) ) , t ∈ ( 0 , 1 ) , u ( 0 ) = 0 , u ( 1 ) = γ u ( η ) , v ( 0 ) = 0 , v ( 1 ) = γ v ( η ) , where α , β , p , q , η , γ satisfy certain conditions.