Behavior of Slip Effects on Oscillating Flows of Fractional Second-Grade Fluid

Authored by: Kashif Ali Abro , Ambreen Siyal , Abdon Atangana

Handbook of Fractional Calculus for Engineering and Science

Print publication date:  February  2022
Online publication date:  February  2022

Print ISBN: 9781032047799
eBook ISBN: 9781003263517
Adobe ISBN:


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This chapter describes slippage of oscillations exhibited by fractional second-grade fluid of varying viscosity. The mathematical model is fractionalized and then tackled by means of Laplace transform. Optimal analytical solutions for velocity and shear stress are investigated using the Wright generalized hypergeometric function. Newtonian and non-Newtonian solutions demonstrate the effect of slipping and non-slipping oscillations of fractional and non-fractional second-grade fluid. Sub-solutions of fractional and non-fractional second-grade fluid are compared for the slippage effects on fluid oscillations. Variable viscosity under the assumption of slip conditions on boundary conditions shows sharp similarities and differences between non-integer and integer mathematical models on the basis of material and embedded parameters.

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