COMPREHENSIVE ANALYSIS OF INTEGER-ORDER, CAPUTO-FABRIZIO (CF) AND ATANGANA-BALEANU (ABC) FRACTIONAL TIME DERIVATIVE FOR MHD OLDROYD-B FLUID WITH SLIP EFFECT AND TIME DEPENDENT BOUNDARY CONDITION

摘要

This article is focused on the slip effect in the unsteady ow ofMHD Oldroyd-B uid over a moving vertical plate with velocity U_of(t). TheLaplace transformation and inversion algorithm are used to evaluate the ex-pression for uid velocity and shear stress. Fractional time derivatives areused to analyze the impact of fractional parameters (memory effect) on thedynamics of the uid. While making a comparison, it is observed that thefractional-order model is best to explain the memory effect as compared to theclassical model. The behavior of slip condition as well as no-slip condition isdiscussed with all physical quantities. The inuence of dimensionless physicalparameters like magnetic force M, retardation time λ_r, fractional parameterff, and relaxation time λ on uid velocity has been discussed through graphicalillustration. Our results suggest that the velocity field decreases by increas-ing the value of the magnetic field. In the absence of a slip parameter, thestrength of the magnetic field is maximum. Furthermore, it is noted that theAtangana-Baleanu derivative in Caputo sense (ABC) is the best to highlightthe dynamics of the uid.