On Nonlinear Evolution Model for Drinking Behavior Under Caputo-Fabrizio Derivative

Jin, Fang; Qian, Zi-Shan; Chu, Yu‐Ming; Rahman, Mati ur

doi:10.11948/20210357

Cited by 88 publications

(39 citation statements)

References 40 publications

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“…The heredity properties, the memory, and the crossover behavior can only be observed in a model with a fractional-order system. The fractional calculus with different fractional operators and their applications have been found, in integrodifferential equations [12] , the development in the operators [13] , [14] , application to epidemiology [15] , [16] , [17] , application to wave dynamics equations, [18] , [19] etc. The COVID-19 model with time delay and stochastic differential equation is explored in [20] .…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling and analysis of COVID-19: A study of new variant Omicron

Khan

Atangana

2022

Physica A: Statistical Mechanics and its Applications

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Section: Introductionmentioning

confidence: 99%

Mathematical modeling and analysis of COVID-19: A study of new variant Omicron

Khan

Atangana

2022

Physica A: Statistical Mechanics and its Applications

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“…The C–C bond makes CNTs in base fluid more effective than other nanocomposite forms. The desired outcome can be obtained by covalent or non-covalent manipulation of CNT nanofluid 34 – 36 . Ferrofluid flow across an endless, impermeable disc was analyzed by Tassaddiq et al 37 .…”

Section: Introductionmentioning

confidence: 99%

Non-Fourier energy transmission in power-law hybrid nanofluid flow over a moving sheet

Alhowaity

Bilal

Hamam

et al. 2022

Sci Rep

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Ethylene glycol is commonly used as a cooling agent in the engine, therefore the study associated with EG has great importance in engineering and mechanical fields. The hybrid nanofluid has been synthesized by adding copper and graphene nanoparticles into the Ethylene glycol, which obeys the power-law rheological model and exhibits shear rate-dependent viscosity. As a result of these features, the power-law model is utilized in conjunction with thermophysical characteristics and basic rules of heat transport in the fluid to simulate the physical situations under consideration. The Darcy Forchhemier hybrid nanofluid flow has been studied under the influence of heat source and magnetic field over a two-dimensionally stretchable moving permeable surface. The phenomena are characterized as a nonlinear system of PDEs. Using resemblance replacement, the modeled equations are simplified to a nondimensional set of ODEs. The Parametric Continuation Method has been used to simulate the resulting sets of nonlinear differential equations. Figures and tables depict the effects of physical constraints on energy, velocity and concentration profiles. It has been noted that the dispersion of copper and graphene nanoparticulate to the base fluid ethylene glycol significantly improves velocity and heat conduction rate over a stretching surface.

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“…Fractional calculus has a memory effect, which aids in correctly predicting physical systems or mathematical models. This has led to new advancements in developing new operators such as Riemann–Liouville-Caputo, Atangana-Baleanu (

), and Caputo–Fabrizio fractional-order derivatives in integer and non-integer orders that have been proposed to be applied to solve real-world problems, for example, the applications in integrodifferential equations [23] , the new advancement and development in fractional operators [24] , [25] , application to epidemiology [26] , [27] , [28] , [29] , [30] , [31] , application to wave dynamics equations, [32] , [33] and other physical problems [34] , [35] , [36] etc. Some recent applications of fractional calculus in physical sciences has been discussed by the authors recently [37] , [38] , [39] .…”

Section: Introductionmentioning

confidence: 99%