The Role of Fox-H Function in Analytic and Fractional Modeling of Helicity of Cylinder: Fractional Generalized Burger Fluid

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 [Formula: see text] 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.

Fractional calculus to control transport phenomena in food engineering: A systematic review of barriers and data agenda

“…In the following centuries, FC applications appeared in problems arising from physics, engineering, mathematics, economics, and other areas (Machado et al, 2014). Nowadays we find models including equations with a fractional differentiation order (e.g., Abro et al, 2020; Hernández et al, 2020).…”