摘要：In this paper we establish an existence result for the multi-term fractional differential equation 1 ( D α m − ∑ i = 1 m − 1 a i D α i ) u ( t ) = f ( t , u ( t ) ) for t ∈ [ 0 , 1 ] , u ( 0 ) = 0 , where D p α m y ( ⋅ ) and D p α i y ( ⋅ ) are fractional pseudo-derivatives of a weakly absolutely continuous and pseudo-differentiable function u ( ⋅ ) : T → E of order α m and α i , i = 1 , 2 , … , m − 1 , respectively, the function f ( t , ⋅ ) : T × E → E is weakly-weakly sequentially continuous for every t ∈ T and f ( ⋅ , y ( ⋅ ) ) is Pettis integrable for every weakly absolutely continuous function y ( ⋅ ) : T → E , T is a bounded interval of real numbers and E is a nonreflexive Banach space, 0 < α 1 < α 2 < ⋯ < α m < 1 and a 1 , a 2 , … , a m − 1 are real numbers such that a : = ∑ i = 1 m − 1 a i Γ ( α m − α i + 1 ) < 1 .
关键词：weak measure of noncompactness ; nonreflexive Banach spaces ; Pettis integral ; multi-term fractional differential equation ; fractional pseudo-derivative
