Keeping in view of the complex fluid mechanics in bio-medicine and engineering, the Burgers’ fluid with a fractional derivatives model analyzed through a rotating annulus. The governing partial differential equation solved for velocity field and shear stress by using integral transformation method and using Bessel equations. The transformed equation inverted numerically by using Gaver-Stehfest’s algorithm. The approximate analytical solution for rotational velocity, and shear stress are presented. The influence of various parameters like fractional parameters, relaxation and retardation time parameters material constants, time and viscosity parameters are drawn numerically. It is found that the relaxation time and time helps the flow pattern, on the other hand other material constants resist the fluid rotation. Fractional parameters effect on fluid flow is opposite to each other. Finally, to check the validity of the solution there are comparisons for velocity field and shear stress for obtained results with an other numerical algorithm named Tzou’s algorithm.

考虑到生物医学和工程中复杂的流体力学，Burgers 流体采用分数导数模型通过旋转环进行分析。利用积分变换方法和贝塞尔方程求解速度场和剪应力的控制偏微分方程。使用Gaver-Stehfest 算法对变换后的方程进行数值反演。给出了旋转速度和剪切应力的近似解析解。各种参数的影响，如分数参数、松弛和延迟时间参数、材料常数、时间和粘度参数都以数字方式绘制。发现弛豫时间和时间有助于流动模式，另一方面，其他材料常数抵抗流体旋转。分数参数对流体流动的影响是相反的。最后，为了检查解的有效性，将获得的结果的速度场和剪应力与另一种名为 Tzou 算法的数值算法进行了比较。