The Windkessel model is a lumped-parameter representation that simplifies the complex cardiovascular system into an equivalent hydraulic circuit comprising resistive and compliant components. It plays a crucial role in understanding the dynamics of blood flow and pressure within the circulatory system, especially in the arterial network. In this study, we employ the Caputo fractional operator to obtain approximate solutions for the Windkessel model within the framework of usual topological Banach spaces. An efficient hybrid analytical technique, termed the Aboodh residual power series method (ARPSM), has been developed by integrating the Aboodh transform with the residual power series method. This approach is used to investigate and derive approximate solutions of the modified Caputo fractional Windkessel model. The accuracy, reliability, and applicability of the proposed ARPSM are demonstrated through numerical and graphical analyses, confirming its effectiveness in solving fractional differential equations of this type.