Abstract This paper focuses on second-order differential equations involving causal operators with nonlinear two-point boundary conditions. By applying the monotone iterative technique in presence of upper and lower solutions, a new comparison theorem, we obtain existence extremal solutions. is an extension classical theory equations. Finally, present two examples to show usefulness our results.

Abstract: This paper is motivated from some recent papers treating the boundary value problems for impulsive fractional differential equations. We first give some notations, recall some concepts and preparation results. Second, we establish a general framework to find the solutions for impulsive fractional boundary value problems, which will provide an effective way to deal with such problems. ...