Adaptive and efficient fractional-order modeling of nonlinear dynamical systems: Addressing memory and order selection challenges

The nonlinear dynamical systems exhibit the long-memory characteristics is not an easy task due to their time-dependent and nonlocal property. The integer-order models cannot represent the memory property of the system, whereas the fixed fractional-order models suffer from inefficiency along with high computational cost. To overcome these problems, in this paper, we propose technique, which incorporates the order adjustment with effective memory reduction. The fractional order ( $\alpha$) is adjusted according to the variation in the system states, allowing the representation of adaptive memory, whereas the redundant components in memory are kept minimum in the process. To validate the proposed approach, the performance was compared with that of the and the fixed models using the well-known Lorenz attractor dataset. It observed that our method the baseline approaches in terms of differences of 0.0376, 0.0294, 4.12%, and $R^2$ score (0.978), respectively. Moreover, the model better ability in preserving the underlying chaotic dynamics.