Some Results for Nonlinear (n+1)-Term Fractional Integrodifferential Inclusions with Multipoint Boundary Conditions

We are concerned with the nonlinear ( n + 1 ) -term fractional integrodifferential inclusions L ( D ) u ∈ F ( t , u , T u , S u ) ,   a . e .   t ∈ [ 0,1 ] , where L ( D ) = D α - b nDβ n- b n - 1Dβ n - 1- ⋯ - b 1Dβ 1, 0 < β 1 < β 2 < ⋯ < β n - 1 < β n < 1 < α < 2 ,b 1 , b 2 , … , b nare constant coefficients, and ( T u ) ( t ) = ∫ 0 1 k ( t , s ) u ( s ) d s , ( S u ) ( t ) = ∫ 0 t l ( t , s ) u ( s ) d s , subject to the nonlocal conditions u ( 0 ) = 0 ,   u ( 1 ) = ∑ i = 1 mγ i u ( η i ) . The existence results are obtained by using two fixed-point theorems due to Bohnenblust-Karlin and Covitz-Nadler, respectively. Our results partly generalize and improve the known ones.