ABSTRACT This study investigates the nonlinear and chaotic dynamics of a modified Hindmarsh–Rose (HR) neuron model through a unified framework based on piecewise fractional differential operators. The classical HR neuron model is widely used to describe the electrical activity of neuronal membranes; however, it does not fully account for memory effects and regime‐switching phenomena observed in real neurobiological processes. To address this limitation, we formulate a piecewise dynamical model in which the membrane potential evolves under different fractional operators, including the Caputo, Atangana–Baleanu, and Caputo–Fabrizio derivatives. A fractional order parameter is introduced to regulate the memory intensity of the system and to construct a generalized fractional‐order HR model. The piecewise structure enables the modeling of switching behaviors and crossover effects between distinct neuronal activity regimes. Numerical simulations are carried out to examine the influence of the fractional order and the piecewise operator structure on neuronal firing patterns, chaotic attractors, and complex oscillatory dynamics under external current stimulation. The numerical results clearly show that changes in the fractional order and the choice of switching thresholds have a pronounced influence on the stability properties, oscillation amplitudes, and chaotic behavior of the neuron model. Through a broad set of numerical experiments, the proposed framework is shown to reliably reproduce key features of neuronal dynamics, demonstrating that the adopted numerical schemes are well suited for capturing memory effects and regime switching. Overall, this study advances fractional and piecewise modeling approaches in neuroscience by providing both new theoretical perspectives and practical computational tools for the investigation of complex neuronal systems.
Kumar et al. (Thu,) studied this question.