Similar transformation solutions of time-fractional robotics equation

This study proposes a self-similar transformation method to solve time-fractional partial differential equations (PDEs) in robotic systems. Unlike conventional models limited to ODEs, our approach captures memory effects and complex dynamics through fractional-order modeling. The reduced form allows analytical treatment while preserving physical behavior. We apply this method to robotic manipulation of acoustic waves, including energy focusing and suppression tasks. The results demonstrate improved prediction accuracy and control performance, offering a promising framework for advanced applications in soft and wave-based robotics.