Unsteady Flow of Immiscible Generalized Second-Grade Fluids in a Rectangular Channel using Fractional Derivatives

Articles in Press

Document Type : Research Paper

Authors

1 1. Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan.\\ 2. Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan.\\ 3. Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah, 64001, Iraq.

2 Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan.

3 Department of Mathematics and Information Technologies, Tashkent State Pedagogical University, Tashkent, Uzbekistan.

4 Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan.

5 Civil and Environmental Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.

Abstract

In this paper, unsteady one-dimensional
ows in a rectangular channel of two incompressible and immiscible
generalized second grade
uids are studied. The generalization discussed consists onto mathematical framework
constructed upon constitutive equations of second-grade (SG)
uid with temporal fractional derivatives Caputo (C),
Caputo-Fabrizio (CF) and Atangna-Baleanu (ABC). The evolution of a shear stress has an impact on the velocity
gradient. The velocity and shear stress components are transformed using a Laplace transformation. The Stehfest's
numerical approach for the reverse Laplace transformation is used to obtain numerical results for actual velocity
and shear stress. The impact of fractional parameters upon velocity and shear stress is investigated using numerical
simulations and graphical depictions. The memory impacts are just noticeable for tiny amounts of time t, according
to this theory.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 20 April 2026

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History

  • Receive Date: 30 June 2025
  • Revise Date: 31 October 2025
  • Accept Date: 14 April 2026

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