# American Institute of Mathematical Sciences

March  2020, 13(3): 683-693. doi: 10.3934/dcdss.2020037

## Analytical results on the unsteady rotational flow of fractional-order non-Newtonian fluids with shear stress on the boundary

 1 Department of Mathematics and statistics, The University of Lahore, Lahore, Pakistan 2 Department of Mathematics, Govt. College University, Lahore, Pakistan 3 Faculty of Sciences and Techniques Errachidia, Moulay Ismail University, Morocco 4 Department of Mathematics, University Of Management and Technology, Lahore, Pakistan

* Corresponding author: Zakia Hammouch, email: hammouch.zakia@gmail.com

Received  May 2018 Revised  November 2018 Published  March 2019

Fund Project: Prof. Zakia Hammouch was supported by the Research Project UMI2016 financed by Moulay Ismail University allowed to team E3MI.

The objective of this paper is to study the unsteady rotational flow of some non Newtonian fluids with Caputo fractional derivative through an infinite circular cylinder by means of the finite Hankel and Laplace transform. The novelty of the work is that motion is produced by applying tangential force not a specific but general function of time on the boundary. Initially the cylinder is at rest and after time $t_{o} = 0^{+}$ it begins to rotate about its axis with an angular velocity $\tau_{o} g(t)$. The obtained solutions of velocity field and shear stress have been presented under series form in terms of generalized $G$-function, satisfying all imposed initial and boundary conditions. The corresponding solutions can be easily particularized to give similar solutions from existing literature for Oldroyd-B fluids, Maxwell fluids, Second grade fluids and Newtonian fluids with/without fractional derivatives performing similar motions.

Citation: Muhammad Mansha Ghalib, Azhar Ali Zafar, Zakia Hammouch, Muhammad Bilal Riaz, Khurram Shabbir. Analytical results on the unsteady rotational flow of fractional-order non-Newtonian fluids with shear stress on the boundary. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 683-693. doi: 10.3934/dcdss.2020037
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