A Fractional Reaction–Diffusion Model for Electroactive Polymer Films: Stability Analysis and Numerical Simulation

The aim of the work is to investigate a nonlinear reaction–diffusion model applied to electroactive polymer films, formulated within a fractional-order framework to incorporate spatial nonlocality and anomalous transport effects. The conventional model is generalized using the Liouville–Caputo fractional derivative to provide a more realistic description of anomalous diffusion. The resulting strongly nonlinear fractional boundary value problem is solved using the Differential Transform Method (DTM), which yields accurate semianalytical approximate solutions. In addition, a detailed perturbation-based stability analysis is performed, leading to an explicit expression for the stability coefficient. The results of the stability analysis clearly show that the system is inherently unstable, and this instability is further amplified by the spatially nonlocal transport effects introduced by the fractional operator. The impact of the fractional order is also investigated, showing that decreasing the fractional order enhances spatial nonlocal interactions and anomalous transport, thereby accelerating the growth of perturbations, whereas the integer-order limit gradually recovers the classical diffusion behavior. The numerical and graphical results are in good agreement with the previously reported results, validate the analytical results, and show the effect of the governing parameters. The proposed analytical framework offers a deeper understanding of the interplay between nonlinearity, saturation, and spatial nonlocal transport in fractional reaction–diffusion systems and provides an efficient methodology for the analysis of complex transport phenomena in electroactive polymer films.