Fractional Derivatives of Some Fractional Functions and Their Applications

“…The study of differential operators of any order is known as fractional calculus, and the viscoelastic behavior of fluids is also described. The Caputo, Caputo-Fabrizio, and Caputo constant proportionality techniques are the most common fractional differentiation approaches [16][17][18]. For steady-state heat conduction, Hristov [19] employed the CF fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Heat and Mass Transfer Analysis of MHD Jeffrey Fluid over a Vertical Plate with CPC Fractional Derivative

et al. 2022

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Free convection flow of non-Newtonian fluids over flat, heated surfaces is an important natural phenomenon that also occurs in human-made engineering processes under various physical and mechanical situations. In the current study, the free convection magnetohydrodynamic flow of Jeffrey fluid with heat and mass transfer over an infinite vertical plate is examined. Mathematical modeling is performed using Fourier’s and Fick’s laws, and heat and momentum equations have been obtained. The non-dimensional partial differential equations for energy, mass, and velocity fields are determined using the Laplace transform method in a symmetric manner. Later on, the Laplace transform method is employed to evaluate the results for the temperature, concentration, and velocity fields with the support of Mathcad software. The governing equations, as well as the initial and boundary conditions, satisfy these results. The impacts of fractional and physical characteristics have been shown by graphical illustrations. The obtained fractionalized results are generalized by a more decaying nature. By taking the fractional parameter β,γ→1, the classical results with the ordinary derivatives are also recovered, making this a good direction for symmetry analysis. The present work also has applications with engineering relevance, such as heating and cooling processes in nuclear reactors, the petrochemical sector, and hydraulic apparatus where the heat transfers through a flat surface. Moreover, the magnetized fluid is also applicable for controlling flow velocity fluctuations.

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“…The fractional calculus is the study of differential operators of the arbitrary order and become a potent too to describe the viscoelastic behavior of the fluids. There are several approaches of fractional differentiation but the most important are Caputo, Caputo-Fabrizio, and constant proportional Caputo (CPC) approaches [1][2][3][4][5][6][7][8]. Hristov [9] investigated the results for transient flow of a non-Newtonian fluid with time space derivative.…”

Section: Introductionmentioning

confidence: 99%

Fractional model of second grade fluid induced by generalized thermal and molecular fluxes with constant proportional caputo

et al. 2021

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In this research article, the constant proportional Caputo approach of fractional derivative is applied to derive the generalized thermal and molecular profiles for flow of second grade fluid over a vertical plate. The governing equations of the prescribed flow model are reduced to dimensionless form and then solved for temperature, concentration, and velocity via Laplace transform. Further graphs of field variables are sketched for parameter of interest. Comparison between present result and the existing results is also presented graphically.

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Fractional Derivatives of Some Fractional Functions and Their Applications

Cited by 12 publications

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Some Formulas of Fractional Trigonometric Functions

Some Formulas of Fractional Trigonometric Functions

Heat and Mass Transfer Analysis of MHD Jeffrey Fluid over a Vertical Plate with CPC Fractional Derivative

Fractional model of second grade fluid induced by generalized thermal and molecular fluxes with constant proportional caputo

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