Approximation Solutions of an Unsteady Fractional Viscoelastic Blood Flow Model in a Compliant Artery
DOI:
https://doi.org/10.56532/mjsat.v6i3.718Keywords:
Fractional calculus, Blood flow, Viscoelasticity, Differential Transform Method (FRDTM), Fractional Variational Iteration Method (FVIM)Abstract
This paper develops and analyzes an unsteady fractional-order blood flow model in a compliant artery by incorporating Caputo fractional derivatives into the classical one-dimensional momentum equation. The fractional formulation accounts for viscoelastic and memory effects that integer-order models cannot adequately describe. Under physiological assumptions of constant blood density, constant viscosity, and a prescribed pressure gradient, approximate analytical solutions are derived using the Fractional Reduced Differential Transform Method (FRDTM). The Fractional Variational Iteration Method (FVIM) is used to validate the FRDTM solutions. Numerical results examine the influence of fractional order, arterial cross-sectional area, and pressure gradient on flow rate. The results indicate that flow rate increases with time for all parameter values and that lower fractional orders demonstrate stronger memory effects compared to higher orders. As the fractional order approaches unity, the model converges toward classical Newtonian behaviour. Close agreement between the results of FRDTM and FVIM confirms the reliability of the proposed method. The findings suggest that fractional modeling provides a more realistic representation of blood flow dynamics in compliant arteries.References
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