ArticleBiomedical engineering and computational biology2026
Fractional Soliton Dynamics in Coupled Myelinated Fibers: Comparative Modeling With Beta, Caputo, and Atangana-Baleanu Derivatives.
Article in Biomedical engineering and computational biology, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
Background: fractional-order modeling provides a powerful framework for representing memory-dependent conduction in excitable biological media. However, existing soliton-based models of myelinated nerve fibers are often theoretical, operator-specific, and insufficiently benchmarked in terms of numerical reproducibility, physiological plausibility, and computational cost. Objectives: This study aims to compare the Liouville-Caputo, Atangana-Baleanu, and Beta fractional operators for modeling soliton-like action-potential propagation in ephaptically coupled myelinated nerve fibers, with emphasis on waveform stability, energy retention, biological consistency, computational efficiency, and adaptive parameter learning. Design: A comparative computational modeling study was conducted using a coupled fractional nonlinear partial differential equation framework, physiological parameter mapping, numerical sensitivity analysis, and physics-informed neural network-based parameter estimation. Methods: A coupled fractional Korteweg-de Vries-type system was solved under identical initial and boundary conditions for the three fractional operators. The time-fractional order α was varied over [0.6, 1.0], while the space-fractional order β was varied over [1.5, 2.0]. Simulations used a uniform spatial grid, fixed time step, localized sech Results: The Beta derivative produced the most localized and stable soliton-like pulses, with stronger amplitude preservation, lower energy loss, and shorter runtime than the Liouville-Caputo and Atangana-Baleanu formulations under the tested settings. Increasing ephaptic coupling strength reduced pulse amplitude, whereas increasing α improved propagation velocity and increasing β enhanced waveform localization. Quantitative residual and error analyses confirmed that the Beta-based formulation maintained low numerical error while preserving biologically plausible conduction behavior. Conclusion: The results support the Beta derivative as a biologically plausible and computationally efficient approximation for soliton-like nerve-pulse propagation in coupled myelinated fibers. The Liouville-Caputo and Atangana-Baleanu operators remain valuable for long-memory and fading-memory regimes, respectively. Future work should integrate literature-constrained biological consistency assessment, stochastic ion-channel dynamics, and heterogeneous multidimensional nerve-bundle geometries.
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