In this paper, the analytic and fractional solutions of governing differential equations for helical flow of cylindrical nature have been presented. The series expansions and Laplace and Hankel transforms are applied to the governing equation of generalized Burger fluid flow for generating gamma functions. The analytical solutions of velocity fields and shear stresses are obtained through Caputo fractional approach. In order to justify the initial and boundary conditions, infinite series are invoked for expressing the analytical results of velocity fields and shear stresses in terms of [Formula: see text] Fox-H function. At the end, few rheological parameters have been analyzed on four different types of models as shown in graphs. Finally, a comparative analysis of ordinary and fractional models has been focussed for angular and oscillating velocities of helical flow generated by circular cylinder.

中文翻译：

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FOX-H 函数在圆柱体螺旋度分析和分式建模中的作用：分式广义汉堡液

本文给出了圆柱型螺旋流控制微分方程的解析解和分数解。级数展开和拉普拉斯和汉克尔变换应用于广义 Burger 流体流动的控制方程以生成伽马函数。通过Caputo分数方法得到速度场和剪切应力的解析解。为了证明初始条件和边界条件的合理性，调用无限级数来表达速度场和剪切应力的分析结果，用 [公式：见文本] Fox-H 函数。最后，如图所示，在四种不同类型的模型上分析了很少的流变参数。最后，