In the present paper, we deal with the existence and multiplicity of solutions for the following impulsive fractional boundary value problem (Formula presemted.). where α∈ (1 / p, 1 ] , 1 < p< ∞, 0 = t0< t1< t2< ⋯ < tn< tn+1= T, f: [ 0 , T] × R→ R and Ij: R→ R, j= 1 , … , n, are continuous functions, (Formula presented). By using variational methods and critical point theory, we give some criteria to guarantee that the above-mentioned impulsive problems have at least one weak solution and a sequences of weak solutions.