<p>This article explores the existence and multiplicity of solutions for a novel class of dynamical systems with fractional derivatives. Unlike classical approaches, we consider a setting where the potential function may lack smoothness, oducing additional analytical challenges. By employing advanced variational methods and critical point theory, we establish the existence of infinitely many nontrivial weak solutions that vanish at infinity, even in the absence of the Palais–Smale compactness condition. These results extend and generalize previous works on fractional dynamical systems, providing new insights into their structure and solution behavior.</p>