Fractional Cosmic String Loops In Expanding Universe

We study the dynamics of circular cosmic string loops in a spatially flat Friedmann Lema\^itre Robertson Walker universe within a fractional Polyakov framework that incorporates nonlocal memory effects. Allowing both the loop radius and polar angle to evolve, we obtain a coupled non-autonomous system governed by string tension, cosmological expansion, and an emergent centrifugal contribution. We show that angular dynamics plays a crucial role in determining the loop evolution. In contrast to standard scenarios where loops collapse, we identify a class of solutions exhibiting sustained expansion driven by dynamically generated angular motion. The system also displays nonlinear behavior with signatures of chaos, with the onset of chaotic dynamics closely correlated with expanding solutions. Our results demonstrate that fractional memory effects and angular degrees of freedom qualitatively modify cosmic string loop dynamics, providing new mechanisms for stability in cosmological backgrounds.