In this work by the index of fixed point and matrix theory, we discuss the positive solutions for the system of Riemann–Liouville type fractional boundary value problems D 0 + α u ( t ) + f 1 ( t , u ( t ) , v ( t ) , w ( t ) ) = 0 , t ∈ ( 0 , 1 ) , D 0 + α v ( t ) + f 2 ( t , u ( t ) , v ( t ) , w ( t ) ) = 0 , t ∈ ( 0 , 1 ) , D 0 + α w ( t ) + f 3 ( t , u ( t ) , v ( t ) , w ( t ) ) = 0 , t ∈ ( 0 , 1 ) , u ( 0 ) = u ′ ( 0 ) = ⋯ = u ( n − 2 ) ( 0 ) = 0 , D 0 + p u ( t ) | t = 1 = ∫ 0 1 h ( t ) D 0 + q u ( t ) d t , v ( 0 ) = v ′ ( 0 ) = ⋯ = v ( n − 2 ) ( 0 ) = 0 , D 0 + p v ( t ) | t = 1 = ∫ 0 1 h ( t ) D 0 + q v ( t ) d t , w ( 0 ) = w ′ ( 0 ) = ⋯ = w ( n − 2 ) ( 0 ) = 0 , D 0 + p w ( t ) | t = 1 = ∫ 0 1 h ( t ) D 0 + q w ( t ) d t , where α ∈ ( n − 1 , n ] with n ∈ N , n ≥ 3 , p , q ∈ R with p ∈ [ 1 , n − 2 ] , q ∈ [ 0 , p ] , D 0 + α is the α order Riemann–Liouville type fractional derivative, and f i ( i = 1 , 2 , 3 ) ∈ C ( [ 0 , 1 ] × R + × R + × R + , R ) are semipositone nonlinearities.
Multiple positive solutions for first-order impulsive integral boundary value problems on time scales
