Abstract
We study a boundary value problem of sequential fractional differential equations equipped with nonlocal integral boundary conditions (strip conditions of finite arbitrary size) involving the first-order derivative of the unknown function. As a variant problem, we discuss a case when nonlocal integral boundary conditions are governed by the unknown function. The existence of solutions for the given problems is investigated by means of some standard tools of fixed point theory. We emphasize that existence results obtained in this paper are new and enrich the existence theory for sequential fractional differential equations. The obtained results are well illustrated with the aid of examples.