Purpose This research aims to enhance the modelling of cardiac rhythm dynamics through the integration of fractional derivatives into Van der Pol oscillators. By employing the Lucas wavelet method (LWM), the study effectively addresses the inherent nonlinearity of cardiac models, providing a more accurate representation of heartbeats, including relaxation, chaos, and bifurcations. The model’s adaptability with two adjustable parameters increases its practical applicability. The performance of LWM is validated through comparisons with the Runge-Kutta fourth-order method, highlighting its reliability. This approach offers potential advancements in computational techniques for understanding and diagnosing cardiovascular conditions. Design/methodology/approach This study employs the LWM to solve Van der Pol-like nonlinear second-order differential equations modelling cardiac rhythm dynamics. The approach incorporates fractional derivatives to capture memory effects and complex temporal dynamics of heartbeats. Operational matrices of Lucas wavelets are used to transform the differential equations into algebraic systems, which are solved numerically. The model’s flexibility is ensured through two adjustable parameters, enhancing its adaptability. The accuracy and reliability of LWM are validated by comparing its results with the Runge-Kutta fourth-order method, demonstrating superior performance in handling nonlinearity and fractional dynamics. Findings The study demonstrates that the LWM effectively approximates solutions for cardiac rhythm models governed by Van der Pol-like nonlinear differential equations. Incorporating fractional derivatives enhances the model’s ability to capture complex cardiac dynamics, including relaxation, chaos, and bifurcations. LWM shows high accuracy and reliability, with error metrics such as RMSE and MAE indicating strong consistency with the Runge-Kutta fourth-order method. Sensitivity analysis reveals that parameters like the pulse shape modification factor and asymmetric damping significantly influence cardiac behaviour. The results highlight LWM’s potential for advancing computational techniques in cardiovascular modelling. Research limitations/implications While the LWM effectively models cardiac rhythm dynamics, the study has limitations. The Van der Pol oscillator, being a phenomenological model, simplifies the heart’s complex physiological processes and does not account for spatial variations in electrical activity. Its ability to simulate pathological conditions like arrhythmias is limited, requiring more complex models for detailed clinical insights. Additionally, the absence of experimental validation restricts the model’s applicability in real-world scenarios. Despite these limitations, the research provides a strong foundation for future studies to enhance cardiac modelling using advanced wavelet-based and fractional-order techniques. Practical implications The study’s findings have significant practical implications for computational cardiology and biomedical engineering. The LWM offers an efficient and accurate approach to modelling cardiac rhythm dynamics, aiding in the analysis of heart conditions such as arrhythmias. Its ability to handle nonlinearities and fractional dynamics makes it suitable for simulating complex cardiac behaviours. The model’s simplicity, with adjustable parameters, enhances its adaptability for various clinical scenarios. This approach can support the development of diagnostic tools, improve the understanding of cardiac disorders, and assist in designing effective treatments and control strategies for cardiovascular diseases. Social implications This research contributes to improving public health by enhancing the understanding of cardiac rhythm disorders through advanced mathematical modelling. The LWM offers insights into heart dynamics, potentially aiding in early diagnosis and more effective management of cardiovascular diseases, which are leading causes of mortality worldwide. By supporting the development of reliable, non-invasive diagnostic tools, the study can help reduce healthcare costs and improve patient outcomes. Additionally, its applications in medical research and education can raise awareness about heart health, contributing to preventive measures and better cardiovascular care in society. Originality/value This research presents a novel approach by integrating fractional derivatives into Van der Pol-like cardiac rhythm models, offering a more comprehensive representation of heart dynamics, including memory effects and complex oscillatory behaviour. The application of the LWM is a key innovation, providing an efficient, accurate, and effective technique for solving nonlinear and fractional differential equations. Unlike traditional methods, LWM effectively handles system nonlinearity and enhances computational performance. The study’s originality lies in its combination of fractional calculus with wavelet-based spectral analysis, offering valuable insights for advancing mathematical modelling in cardiovascular research.
R. Rajaraman (Wed,) studied this question.