How to precisely characterize the fractional modeling and physical treatment is an ongoing challenge in fluid mechanics and numerical techniques, especially in nonlinear complex models. A model study is conducted to report fractional time-dependent mixed convection incompressible fluid flow inside a channel. The physical system is under the impacts of viscous dissipation, electrical and magnetic fields. Three fractional operators Atangana Baleanu Caputo (ABC), Caputo Fabrizio (CF), and classical Caputo (CC) are involved into the temporal derivative. Transformations are used to convert the physical model into equivalent fractional partial differential equations (FPDEs). The computational code is developed for finite difference schemes and code validation is made for different fractional operators. The simulations have been performed to check the appropriate fractional operator and a comparison is made to check the accuracy and efficiency. Additionally, a set of graphs is asserted to show the velocity and temperature distribution for various values of parameters. Velocity is analyzed as decreasing function with an enhancement in the Rayleigh number while the higher fractional parameter (α) causes a dominant drop. A dropped velocity is analyzed in the absence of oscillation and enhanced velocity for higher oscillation, while a more dominant increment in the velocity is noted when Λ₀ is non-zero. A decrease in the thermal layer is observed for higher Pe, and a more dominant impact is noted for smaller values of the fractional parameter. The pattern of the thermal profile is observed enhancing when there is an involvement of radiative parameter while lower temperature distribution is noted in the absence of the radiative term.

如何精确表征分数建模和物理处理是流体力学和数值技术中的一个持续挑战，特别是在非线性复杂模型中。进行模型研究以报告通道内的分数时间相关混合对流不可压缩流体流动。物理系统受到粘性耗散、电场和磁场的影响。时间导数涉及三个分数运算符 Atangana Baleanu Caputo (ABC)、Caputo Fabrizio (CF) 和经典 Caputo (CC)。转换用于将物理模型转换为等效的分数偏微分方程（FPDE）。计算代码是为有限差分方案开发的，并且代码验证是针对不同的分数运算符进行的。已执行模拟以检查适当的分数运算符，并进行比较以检查准确性和效率。此外，还断言了一组图表以显示各种参数值的速度和温度分布。速度被分析为随着瑞利数的增加而减少的函数，而较高的分数参数 (α) 导致显着下降。在没有振荡的情况下分析下降的速度，并为更高的振荡增加速度，而当 Λ ₀非零时，注意到速度的更主要增量。对于较高的Pe ，观察到热层减少，并且对于较小的分数参数值，注意到更显着的影响。当涉及辐射参数时，观察到热剖面的模式会增强，而在没有辐射项的情况下会注意到较低的温度分布。