On the Stability of Fractional Differential Equations Involving Generalized Caputo Fractional Derivative

Tran, Minh Duc; Vu, Ho; Van, Hoa Ngo

doi:10.1155/2020/1680761

Cited by 10 publications

(8 citation statements)

References 23 publications

(30 reference statements)

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“…Seth et al (2015) discussed the MHD natural convection flow over an exponentially accelerated vertical plate with heat absorption. Tran et al (2020) worked on stability of fractional derivatives for fractional calculus equations, Tuan et al (2020) studied the mathematical model used for transference of COVID-19 with Caputo fractional derivatives. Shateyi et al (2011) discussed the…”

Section: Introductionmentioning

confidence: 99%

MHD Flow of Jeffrey Fluid With Heat Absorption and Thermo-Diffusion

Ramzan¹,

Shafique²,

Ikram³

et al. 2023

Front. Heat Mass Transf.

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Unsteady flow of fractionalized Jeffrey fluid over a plate is considered. In addition, thermo diffusion and slip effects are also used in the problem. The flow model is solved using Constant proportional Caputo fractional derivative. Initially, the governing equations are made non-dimensional and then solved by Laplace transform. From the Figs., it is observed that Prandtl and Smith numbers have decreasing effect on fluid motion, whereas thermodiffusion have increasing effect on fluid motion. Moreover, comparison among fractionalized and ordinary velocity fields is also drawn.

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Section: Introductionmentioning

confidence: 99%

MHD Flow of Jeffrey Fluid With Heat Absorption and Thermo-Diffusion

Ramzan¹,

Shafique²,

Ikram³

et al. 2023

Front. Heat Mass Transf.

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show abstract

“…Seth et al, [21] discussed the MHD convection flow over a vertical plate with ramped temperature. Tran et al, [22] studied on mandatory stability of fractional derivatives for fractional calculus equations, and the mathematical model used for transference of COVID-19 with Caputo fractional derivatives also discussed by Tuan et al, [23].…”

Section: Introductionmentioning

confidence: 99%

Unsteady Magnetohydrodynamic Flow of Second Grade Nanofluid (Ag-Cu) With CPC Fractional Derivative

Shafique

Ramzan

Nisa

et al. 2022

ARFMTS

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Unsteady magnetohydrodynamics (MHD) flow of fractionalized second grade nanofluid (Ag-Cu) over a vertical plate is obtained. The model is solved by using CPC fractional derivative. The novelty of present study is to generalized the model by using Fourier’s and Fick’s laws. The nanofluids are formed by dispersing two different nanoparticles, silver (Ag) and copper (Cu), into a based fluid. The governing dimensionless equations for velocity, concentration, and temperature profiles are solved using Laplace transform method and compared graphically. The effects of different parameters like fractional parameter, second grade parameter and magnetic parameter M are discussed through numerous graphs. From figures, it is observed that second grade and magnetic field have decreasing effect on velocity profile, whereas mass Grashof number have increasing effect on velocity of fluid.

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“…Seth et al, [21] discussed the MHD convection flow over a vertical plate with ramped temperature. Tran et al, [22] worked on mandatory stability of fractional derivatives for fractional calculus equations, and the mathematical model used for transference of COVID-19 with Caputo fractional derivatives also discussed by Tuan et al, [23].…”

Section: Introductionmentioning

confidence: 99%

Slippage Flow of Maxwell Fluid Over an Inclined Vertical Plate With Generalized Heat and Mass Transfer

Shafique

Rasid

Nazar

et al. 2022

ARFMTS

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In this paper, unsteady flow of fractionalized Maxwell fluid over an inclined vertical plate is considered by using thermo diffusion and slip effects. The flow model is solved using Constant proportional Caputo fractional derivative. Initially, the governing equations are made non-dimensional and then solved by Laplace transform. To see the impact of different flow parameters on the velocity, temperature and concentration, we have drawn some graphs. In addition, it is observed that magnetic field has decreasing effect on fluid motion whereas thermo-diffusion have increasing effect on fluid motion.

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On the Stability of Fractional Differential Equations Involving Generalized Caputo Fractional Derivative

Cited by 10 publications

References 23 publications

MHD Flow of Jeffrey Fluid With Heat Absorption and Thermo-Diffusion

MHD Flow of Jeffrey Fluid With Heat Absorption and Thermo-Diffusion

Unsteady Magnetohydrodynamic Flow of Second Grade Nanofluid (Ag-Cu) With CPC Fractional Derivative

Slippage Flow of Maxwell Fluid Over an Inclined Vertical Plate With Generalized Heat and Mass Transfer

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