Sequential fractional differential equations and unification of anti-periodic and multi-point boundary conditions

In this paper, we present a novel idea of unification of anti-periodic and multi-point boundary conditions and develop the existence theory for sequential fractional differential equations supplemented with these new conditions. We apply fixed point theorems due to Banach, Krasnoselskii, Leray-Schauder alternative criterion, and Leray-Schauder degree theory to obtain the desired results. Our results are well-illustrated with the aid of examples and correspond to some new special cases for particular choices of parameters involved in the problem.