On Solving Caputo Fractional Windkessel Model with System of Cardiovascular Circulatory by Using Some Residual Maps Technique

Abstract

The Windkessel model provides a simplified framework for representing the cardiovascular system, emphasizing the role of arterial elasticity. It elucidates how the compliance of major arteries smooths the heart’s pulsatile pumping, resulting in a steadier blood flow. This work utilizes the Caputo fractional operator to derive analytical solutions for the Windkessel model within standard topological Banach spaces. We introduce a novel approach called the Sawi Residual Power Series Technique (SRPST), which combines the Sawi transform with the residual power series method. This technique allows for a thorough investigation of the modified Caputo fractional Windkessel model. Our studies demonstrate the efficiency, reliability, and capability of SRPST in deriving analytical solutions, supported by various numerical and graphical analyses. The results not only validate the proposed method but also highlight its potential applications in broader fields such as fluid dynamics and biomedical engineering.