This paper is structured in two parts, both focusing on the analysis of nonlinear coupled systems using fractional calculus. In the first part, we study a beam deflection-type system with sequential Caputo derivatives. We prove an existence and uniqueness result under nonlocal boundary conditions by applying Banach’s fixed point theorem. Additionally, we discuss the Ulam-Hyers stability of the system, supported by illustrative examples. In the second part, we apply the Tanh method to obtain travelling wave solutions for a coupled evolution system related to the sequential model.