<![CDATA[This study presents an extended fractional Maxwell fluid model for pulsatile blood flow through a stenosed artery by incorporating the combined effects of a magnetic field, porous medium, chemical reaction, heat source, and suspended nanoparticles. Blood is modeled as a compressible, viscoelastic, and electrically conducting fluid, and the governing fractional-order coupled nonlinear partial differential equations for momentum, energy, and nanoparticle concentration are formulated in cylindrical coordinates. To capture fluid memory effects, the Caputo fractional derivative is employed, and the resulting system is solved semi-analytically using the Laplace transform method. The inverse Laplace transforms, involving modified Bessel functions, are computed numerically through the Concentrated Matrix-Exponential method implemented in Python to improve stability and accuracy. Validation against existing literature demonstrates excellent agreement. The parametric results show that increasing the Hartmann number, stenosis length, particle mass, and chemical reaction parameter reduces both velocity and nanoparticle concentration, whereas higher heat source, Peclet number, and nanoparticle concentration parameters enhance flow and particle dispersion. The findings further indicate that fractional-order effects strongly influence velocity behavior, with lower fractional orders producing stronger memory effects and smoother gradients. The study concludes that the proposed model improves the prediction of hemodynamic behavior under pathological arterial conditions and offers useful implications for magnetic-assisted therapies and nanoparticle-based drug delivery.]]>
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