Piecewise Optimal Fractional Reproducing Kernel Solution and Convergence Analysis for the Atangana–baleanu–caputo Model of the Lienard’s Equation

Momani, Shaher; Arqub, Omar Abu; Maayah, Banan

doi:10.1142/s0218348x20400071

Cited by 106 publications

(29 citation statements)

References 31 publications

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“…An ongoing work is trying to tackle the problem regarding those aspects. The model can also be extended using the promising theory of fractional calculus [ 1 , 2 , 5 , 6 , 59 , 60 , 64 ].…”

Section: Discussionmentioning

confidence: 99%

Estimation and optimal control of the multiscale dynamics of Covid-19: a case study from Cameroon

et al. 2021

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“…An ongoing work is trying to tackle the problem regarding those aspects. The model can also be extended using the promising theory of fractional calculus [ 1 , 2 , 5 , 6 , 59 , 60 , 64 ].…”

Section: Discussionmentioning

confidence: 99%

Estimation and optimal control of the multiscale dynamics of Covid-19: a case study from Cameroon

et al. 2021

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“…Hayat et al, 34 Pal and Mondal 35 examined the impact of MHD and heat (source/sink) on 3D water based nanofluid flow. Interesting results of nanofluid flow through stretching surface in the presence of MHD and thermal radiation were communicated by Ramzan et al 36 Furthermore, additional interesting and recent studies on MHD and RK-4 method can be seen in Arqub and Rashaideh, 37 Arqub, 38 and Momani et al 39 Having inspired from the above mention perceptions, in this work we have represented the consequence of MHD on unsteady flow of nanofluids over a rotating frame. An advanced type of nanoliquid, which consists of cylindrical shape nano materials CNTs is being taken into an account.…”

Section: Introductionmentioning

confidence: 90%

Magneto hydrodynamic and dissipated nanofluid flow over an unsteady turning disk

Gul

Usman

Khan

et al. 2021

Advances in Mechanical Engineering

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A modern development in the field of fluid dynamics emphasizes on nanofluids which maintain remarkable thermal conductivity properties and intensify the transport features of heat in fluids. The present communication provides an innovative idea of MHD (magneto-hydrodynamics) unsteady, incompressible nanoliquid flow due to the stretching rotating disk with the effect of Joule heating and dissipation. The engine oil is used as a carrier fluid for an immersed rotating disk. A special type of nanoliquid, which consists of cylindrical shape nano materials CNTs (Carbon Nanotubes), is being taken into an account. The CNTs are assembled of both single and multi-walled carbon nanotubes. Some other factors such as the effect of joule heating and viscus dispassion are also used in this investigation. The foremost set of PDEs (Partial Differential Equations) of our model is reformed to the dimensionless form via invoking suitable variables. The resultant set of equations is sketched out through RK-4 method. Furthermore, the velocity profile and energy distribution versus dimensionless flow factors have been sketched and discussed. Also, the outcomes of important engineering curiosity like Nusselt number and skin friction are depicted and interpreted by taking various model factors. Radial and transverse velocity fields, declines via [Formula: see text] (magnetic factor), while the temperature field enhances. Furthermore, the larger estimation of [Formula: see text] leads to enhance the velocity field while higher estimation of [Formula: see text] reducing the velocity and temperature fields. The current work has an extensive verity use such as nano-mechanics and electro-magnetic micro pumps.

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“…Mathematical models and differential equations have great importance in understanding ecological problems [1][2][3] as well as problems in the other stream of applied mathematics [4][5][6][7]. In ecological models, predator-prey systems have attracted many researchers and particularly, in the recent years, stage-structured predator-prey models with time delays have achieved remarkable attention [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…Fig 5. Bifurcation diagram for delay τ 1 : I, II and III represent equilibrium x, y A and y J respectively.…”

mentioning

confidence: 99%

Predator–prey system with multiple delays: prey’s countermeasures against juvenile predators in the predator–prey conflict

Kaushik

Banerjee

2021

J. Appl. Math. Comput.

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Usually, juvenile predators are small in size, comparatively feeble and in the earlier phase of learning the tricky manoeuvre skills of predation. Due to small prey-predator size-ratio, juvenile predators and preys become two deadliest opponents, therefore, whenever both face off, the outcome may be utterly unpredictable. In response to the juvenile predators' attack, preys also come up with a countermeasure and try to defend themselves but a sharp role-reversal in the predator-prey ecology occurs when preys kill the juvenile predators during the counter-attacking strategies. In this paper, we propose and analyze a biologically motivated delayed predator-prey system to explore the joint impact of counterattacking strategies and multiple delays on the predator-prey interactions. We have introduced the transformation of immature to mature predators including delay τ 1 as an average time to reach maturity. Another time delay τ 2 owing to the gestation of the adult predators, is taken into account. After the brief discussion of the basic ecosystem properties for the model in absence of delay, we have performed the stability analysis of the delayed system comprehensively. In this context, existence of Hopf bifurcation at the interior equilibrium is established and its stability as well as direction of the Hopf bifurcation is also investigated. Numerical simulations are also performed to corroborate the theoretical findings. Through this work, it has been illustrated that counterattacking of preys suppresses the unstable oscillations in the population, on the other hand, large delays always destabilize the interior steady state. Hence, in the realistic predator-prey ecology, where counterattack and delays are showing opposite behavior in the same ecosystem, the results of this paper are important to disclose the actual crossover and synergies between both the ecological properties.

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Piecewise Optimal Fractional Reproducing Kernel Solution and Convergence Analysis for the Atangana–baleanu–caputo Model of the Lienard’s Equation

Cited by 106 publications

References 31 publications

Estimation and optimal control of the multiscale dynamics of Covid-19: a case study from Cameroon

Estimation and optimal control of the multiscale dynamics of Covid-19: a case study from Cameroon

Magneto hydrodynamic and dissipated nanofluid flow over an unsteady turning disk

Predator–prey system with multiple delays: prey’s countermeasures against juvenile predators in the predator–prey conflict

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