ArticleOpen Access

THE ROLE OF FOX-H FUNCTION IN ANALYTIC AND FRACTIONAL MODELING OF HELICITY OF CYLINDER: FRACTIONAL GENERALIZED BURGER FLUID

KASHIF ALI ABRO

Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan

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ILYAS KHAN

Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

E-mail Address: ilyaskhan@tdtu.edu.vn

Corresponding author.

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, and

KOTTAKKARAN SOOPPY NISAR

Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser, 11991, Saudi Arabia

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https://doi.org/10.1142/S0218348X20400502Cited by:10 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

In this paper, the analytic and fractional solutions of governing differential equations for helical flow of cylindrical nature have been presented. The series expansions and Laplace and Hankel transforms are applied to the governing equation of generalized Burger fluid flow for generating gamma functions. The analytical solutions of velocity fields and shear stresses are obtained through Caputo fractional approach. In order to justify the initial and boundary conditions, infinite series are invoked for expressing the analytical results of velocity fields and shear stresses in terms of $H_{a, b + 1}^{1, a} (z)$ Fox-H function. At the end, few rheological parameters have been analyzed on four different types of models as shown in graphs. Finally, a comparative analysis of ordinary and fractional models has been focussed for angular and oscillating velocities of helical flow generated by circular cylinder.

Keywords:

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Vol. 28, No. 08

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Received 7 January 2019

Accepted 26 February 2020

Published: August 10, 2020

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This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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THE ROLE OF FOX-H FUNCTION IN ANALYTIC AND FRACTIONAL MODELING OF HELICITY OF CYLINDER: FRACTIONAL GENERALIZED BURGER FLUID

Abstract

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