Mathematical analysis of coupled systems with fractional order boundary conditions

In this paper, we prove the existence, uniqueness and various kinds of Ulam stability for fractional order coupled systems with fractional order boundary conditions involving Riemann-Liouville fractional derivatives. The standard fixed point theorem like Leray-Schauder alternative and Banach contraction are applied to establish the existence theory and uniqueness. Furthermore, we build sufficient conditions for the stability mentioned above by two methods. Also, an example is given to illustrate our theoretical results. The proposed problem is the generalization of third-order ordinary differential equations with classical, initial and anti-periodic boundary conditions.