The Caputo fractional Windkessel model and cardiovascular circulatory system: Some approximate solutions in usual topological Banach spaces by using some techniques

Faten H. Damag; Faten H. Damag

doi:10.3934/math.20251261

AIMS Mathematics

2025, Volume 10, Issue 12: 28651-28667. doi: 10.3934/math.20251261

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Research article

The Caputo fractional Windkessel model and cardiovascular circulatory system: Some approximate solutions in usual topological Banach spaces by using some techniques

Faten H. Damag ^{1,2
,
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1.
Department of Mathematics, Faculty of Sciences, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Mathematics, Faculty of Applied Sciences, Taiz University, Taiz 6803, Yemen

Received: 20 August 2025 Revised: 29 October 2025 Accepted: 24 November 2025 Published: 04 December 2025
MSC : Primary 44A10, 33B15, 34A34, 35A20

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.
- Residual power series,
- Aboodh transform,
- Caputo derivative operator
Citation: Faten H. Damag. The Caputo fractional Windkessel model and cardiovascular circulatory system: Some approximate solutions in usual topological Banach spaces by using some techniques[J]. AIMS Mathematics, 2025, 10(12): 28651-28667. doi: 10.3934/math.20251261

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Abstract

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.

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