Fractional calculus has shown good adaptability in describing the mechanical properties of viscoelastic materials. Based on fractional order theory, the characteristics of blood flow in the fractal network of blood vessels are analyzed, and experiments are carried out by using a mixed solution to prove the results of simulation analysis that contains glycerol, gelatin, sodium chloride, etc. Under different time of fractional order conditions, the effects of Reynolds number, vascular network fractal dimension, and bifurcation series conditions, the blood flow characteristics in fractal vascular network are analyzed. The analysis results show that the blood flow increases with the increase in time fractional order and the flow resistance decreases with the increase in time fractional order. The blood flow law curve based on the equivalent Casson fluid theory has the same trend between the orders α = 0.9 and α = 1.0 of the time fractional order curve, so the order of time fractional order can describe the blood flow characteristics of equivalent Casson fluid. The experimental data are distributed on both sides of the theoretical calculation curve and the relative error is small, which is in good agreement with the effect of vascular fractal parameters obtained by integer order on blood.

中文翻译：

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基于时间分数阶的分形血管网络血流特征分析

小数演算在描述粘弹性材料的机械性能方面显示出良好的适应性。基于分数阶理论，分析了血管分形网络中的血流特征，并通过混合溶液进行了实验，以证明包含甘油，明胶，氯化钠等的模拟分析结果。分析了分数阶条件的不同时间，雷诺数，血管网络分形维数和分叉级数条件的影响，分析了分数维网络的血流特征。分析结果表明，随着时间分数阶数的增加，血流增加，而随着时间分数阶数的增加，血流阻力减小。基于等效Casson流体理论的血流定律曲线在时间分数阶曲线的阶数α= 0.9和α= 1.0之间具有相同的趋势，因此时间分数阶的阶数可以描述等效Casson流体的血流特性。实验数据分布在理论计算曲线的两侧，相对误差较小，与整数阶获得的血管分形参数对血液的影响吻合良好。