Second-grade fluid with Newtonian heating under Caputo fractional derivative: analytical investigations via Laplace transforms

Sene, Ndolane

doi:10.53391/mmnsa.2022.01.002

Cited by 29 publications

(12 citation statements)

References 36 publications

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“…We substitute (14) for n � 0 into (15) and (17) Similarly, for n � 1 to n � n + 1, we have as follows:…”

Section: Variables/parameters Valuementioning

confidence: 99%

“…e fractional order model gives a better description of the entire space of a system; unlike the integer model that describes only the local properties of a system, it also gives a better description of a real system with memory effects [15][16][17][18]. e Caputo derivative and the Riemann-Liouville derivative are regarded as singular kernels fractional derivative relative to biological problems, we also have others which are nonsingular such as Mittag-Leffler and the Atangana-Baleanu operators [17,19]. e fractional order and classical derivatives have been used in studying transmission dynamics in SIR models and the like, but it has not been adopted in an SIT model.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Solution of the Fractional Order Sterile Insect Technology Model via the Laplace–Adomian Decomposition Method for the Spread of Zika Virus Disease

Atokolo

Aja

Aniaku

et al. 2022

International Journal of Mathematics and Mathematical Sciences

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Sterile insect technology (SIT) is an environmental-friendly method which depends on the release of sterile male mosquitoes that compete with the wild male mosquitoes and mate with wild female mosquitoes, which leads to the production of no offspring and as such reduces the population of Zika virus vector population over time, thereby eliminating the spread of Zika virus in a population. The fractional order sterile insect technology (SIT) model to reduce the spread of Zika virus disease is considered in this present work. We employed the use Laplace–Adomian decomposition method (LADM) to determine an analytical (approximate) solution of the model. The Laplace–Adomian decomposition method (LADM) produced a solution in form of an infinite series that further converges to the exact value. We compared solutions of the fractional model with the classical case using our plots and discovered that the fractional order has more degree of freedom and as such the system can be varied to get many preferred responses of the different classes of the model as the fraction (β) could be varied to the desired rate, say 0.7, 0.4, etc. We have been able to show that LADM can be used to solve an SIT model which has never been done before in literature.

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“…We substitute (14) for n � 0 into (15) and (17) Similarly, for n � 1 to n � n + 1, we have as follows:…”

Section: Variables/parameters Valuementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximate Solution of the Fractional Order Sterile Insect Technology Model via the Laplace–Adomian Decomposition Method for the Spread of Zika Virus Disease

Atokolo

Aja

Aniaku

et al. 2022

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

show abstract

“…Fractional calculus represents the generalization of integrals and derivatives to non-integer order. After Leibniz fractional calculus has gained increasing popularity and finds applications in various fields of science, technology and medicine [18,19,20,21,22,23]. Recently, Ozkose and Yavuz [24] in their paper studied in fractional-order case the relations between COVID-19 and diabetes diseases under the hereditary traits then validated their model by the real data from Turkey.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional fractional system with the stability condition and chaos control

Gholami

Ghaziani

Eskandari

2022

mmnsa

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A three-dimensional system is introduced in this paper and its local stability is analyzed. Our study establishes the validity and uniqueness of the linear feedback control for the proposed system and proves its existence and uniqueness. The numerical simulation algorithm described by Atanackovic and Stankovic is finally applied. The analytical results are analyzed and the dynamics of the system are explored in more detail.

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“…The results showed that MHD and Rayleigh number influence the flow behavior. By assessing the literature papers [50][51][52][53][54][55][56][57], it has been found that convection and finite element methods are described.…”

Section: Introductionmentioning

confidence: 99%

Impact of Non-Uniform Periodic Magnetic Field on Unsteady Natural Convection Flow of Nanofluids in Square Enclosure

et al. 2022

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In this article, unsteady free convective heat transport of copper-water nanofluid within a square-shaped enclosure with the dominance of non-uniform horizontal periodic magnetic effect is investigated numerically. Various nanofluids are also used to investigate temperature performance. The Brownian movement of nano-sized particles is included in the present model. A sinusoidal function of the y coordinate is considered for the magnetic effect, which works as a non-uniform magnetic field. The left sidewall is warmed at a higher heat, whereas the right sidewall is cooled at a lower heat. The upper and bottom walls are insulated. For solving the governing non-linear partial differential equation, Galerkin weighted residual finite element method is devoted. Comparisons are made with previously published articles, and we found there to be excellent compliance. The influence of various physical parameters, namely, the volume fraction of nanoparticles, period of the non-uniform magnetic field, Rayleigh number, the shape and diameter of nanoparticles, and Hartmann number on the temperature transport and fluid flow are researched. The local and average Nusselt number is also calculated to investigate the impact of different parameters on the flow field. The results show the best performance of heat transport for the Fe3O4-water nanofluid than for other types of nanofluids. The heat transport rate increases 20.14% for Fe3O4-water nanofluid and 8.94% for TiO2-water nanofluid with 1% nanoparticles volume. The heat transportation rate enhances with additional nanoparticles into the base fluid whereas it decreases with the increase of Hartmann number and diameter of particles. A comparison study of uniform and non-uniform magnetic effects is performed, and a higher heat transfer rate is observed for a non-uniform magnetic effect compared to a uniform magnetic effect. Moreover, periods of magnetic effect and a nanoparticle’s Brownian movement significantly impacts the temperature transport and fluid flow. The solution reaches unsteady state to steady state within a very short time.

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Second-grade fluid with Newtonian heating under Caputo fractional derivative: analytical investigations via Laplace transforms

Cited by 29 publications

References 36 publications

Approximate Solution of the Fractional Order Sterile Insect Technology Model via the Laplace–Adomian Decomposition Method for the Spread of Zika Virus Disease

Approximate Solution of the Fractional Order Sterile Insect Technology Model via the Laplace–Adomian Decomposition Method for the Spread of Zika Virus Disease

Three-dimensional fractional system with the stability condition and chaos control

Impact of Non-Uniform Periodic Magnetic Field on Unsteady Natural Convection Flow of Nanofluids in Square Enclosure

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