Numerical exploration of thin film flow of MHD pseudo-plastic fluid in fractional space: Utilization of fractional calculus approach

Qayyum, Mubashir; Ismail, Fudziah; Sohail, Muhammad; Imran, Naveed; Askar, Sameh; Park, Choonkil

doi:10.1515/phys-2021-0081

Cited by 26 publications

(8 citation statements)

References 47 publications

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“…The work has a large variety of products in biomedical science. Through the use of a homotopy-based approach and fractional calculus, the thin film flow of non-Newtonian pseudo-plastic liquid on a vertical wall was examined 6 . Additionally, in fractional space, the effect of numerous factors on speed was also investigated.…”

Section: Introductionmentioning

confidence: 99%

Peristaltic transport of Rabinowitsch nanofluid with moving microorganisms

Moatimid

Mohamed

Elagamy

2023

Sci Rep

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The key objective of the current examination is to examine a symmetrically peristaltic movement of microorganisms in a Rabinowitsch fluid (RF). The Boussinesq approximation, buoyancy-driven flow, where the density with gravity force term is taken as a linear function of heat and concentrations, is kept in mind. The flow moves with thermophoretic particle deposition in a horizontal tube with peristalsis. The heat distribution and volume concentration are revealed by temperature radiation and chemical reaction characteristics. The originality of the existing study arises from the importance of realizing the benefits or the threats that nanoparticles, microbes, and bacteria cause in the flow inside peristaltic tubes. The results are an attempt to understand what factors perform additional advantages and or reduce damages. The controlling nonlinear partial differential equations (PDEs) are made simpler by employing the long wavelength (LWL) and low-Reynolds numeral (LRN) approximations. These equations are subjected to a set of non-dimensional transformations that result in a collection of nonlinear ordinary differential equations (ODEs). By employing the Homotopy perturbation method (HPM), the configuration of equational analytical solutions is examined. Analytical and graphical descriptions are provided for the distributions of axial speed, heat, microbes, and nanoparticles under the influence of these physical characteristics. The important findings of the current work may help to comprehend the properties of several variations in numerous biological situations. It is found that the microorganisms condensation decays with the rise of all the operational parameters. This means that the development of all these factors benefits in shrinking the existence of harmful microbes, viruses, and bacteria in the human body’s peristaltic tubes, especially in the digestive system, and large and small intestines.

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Section: Introductionmentioning

confidence: 99%

Peristaltic transport of Rabinowitsch nanofluid with moving microorganisms

Moatimid

Mohamed

Elagamy

2023

Sci Rep

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“…In recent years, the fractional derivative has attracted much attention because of its advantages in describing the complex phenomena occuring in the extreme environments such as the nonsmooth boundary, [21][22][23] microgravity, [24][25][26] fractal media, [27][28][29] porous medium, 30,31 and so on. [32][33][34][35][36][37][38][39][40] The local fractional derivative (LFD), [41][42][43][44] which is a new definition of the fractional derivative, has been shown to have many applications in different fields involving in diffusion, 45 Burgers, 46 oscillators, 47 waves, 48 circuits, 49,50 and so on. [51][52][53] Inspired by the latest research of the LFD, in this work, we aim to study a new (2 + 1)-dimensional local fractional breaking soliton equation (LFBSE) as…”

Section: Introductionmentioning

confidence: 99%

“…It is of great significance to study the exact solution of the NLPDEs since it can enable us to better understand and make use of natural phenomena. In recent years, the fractional derivative has attracted much attention because of its advantages in describing the complex phenomena occuring in the extreme environments such as the nonsmooth boundary, 21–23 microgravity, 24–26 fractal media, 27–29 porous medium, 30,31 and so on 32–40 . The local fractional derivative (LFD), 41–44 which is a new definition of the fractional derivative, has been shown to have many applications in different fields involving in diffusion, 45 Burgers, 46 oscillators, 47 waves, 48 circuits, 49,50 and so on 51–53 .…”

Section: Introductionmentioning

confidence: 99%

On the non‐differentiable exact solutions of the (2 + 1)‐dimensional local fractional breaking soliton equation on Cantor sets

Wang

2022

Math Methods in App Sciences

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In this article, a new (2 + 1)‐dimensional local fractional breaking soliton equation is derived with the local fractional derivative. Applying the traveling wave transform of the non‐differentiable type, the (2 + 1)‐dimensional local fractional breaking soliton equation is converted into a nonlinear local fractional ordinary differential equation. By defining a set of elementary functions on Cantor sets, a novel analytical technique namely the Mittag–Leffler function‐based method is employed for the first time ever to construct the exact solutions. The solutions on the Cantor sets are presented via the 3‐D contours. It reveals that the proposed method is effective and powerful and is expected to give some inspiration for the study of the local fractional PDEs.

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“…For the first time, Qayyum et al [41] have been performed the homotopy-based fractional analysis of thin film flow of pseudo-plastic fluid on a vertical. They comprehensively considered three cases to solve the problem of different parameter values.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis and Optimal Control of Rumor Propagation Model with Reporting Effect

Pan

Yan

et al. 2022

Advances in Mathematical Physics

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Media reports and the number of rumors in the media have an important impact on the spread of rumors. Currently, studies that consider these two factors comprehensively on rumor propagation are uncommon. It is better to consider both effects comprehensively than to consider one of them alone. In this paper, we established a new propagation model, which regards the number of rumors in the media as a subclass that changes with time, and then comprehensively considered the effect of these two factors on the process of rumor propagation. We proved the existence and stability of equilibrium points of the model. Then, we selected two reasonable control variables: science popularization intensity and punishment intensity. We find that the control effects are optimal when these two control variables take the maximum value. Theoretical analysis and numerical simulation results showed that positive media publicity can reduce the spread of rumors, but cannot stop the spread of rumors. And under the parameters given in this paper, the optimal control parameter values satisfying the constraints can be calculated through quantitative analysis. This method provided a new idea for studying the optimal control of rumor propagation.

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Numerical exploration of thin film flow of MHD pseudo-plastic fluid in fractional space: Utilization of fractional calculus approach

Cited by 26 publications

References 47 publications

Peristaltic transport of Rabinowitsch nanofluid with moving microorganisms

Peristaltic transport of Rabinowitsch nanofluid with moving microorganisms

On the non‐differentiable exact solutions of the (2 + 1)‐dimensional local fractional breaking soliton equation on Cantor sets

Dynamic Analysis and Optimal Control of Rumor Propagation Model with Reporting Effect

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