文摘
We obtain some existence and uniqueness results for an impulsively hybrid fractional quantum Langevin (qk-difference) equation involving a new qk -shifting operator aΦqk(m)=qkm+(1−qk)a and supplemented with non-separated boundary conditions containing Caputo qk-fractional derivatives. Our first result, relying on Banach’s fixed point theorem, is concerned with the existence of a unique solution of the problem. The existence results are established by means of Leray–Schauder nonlinear alternative and a fixed point theorem due to O’Regan. We construct some examples for the applicability of the obtainedresults. The paper concludes with interesting observations.