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    Brownian motion and thermophoretic diffusion impact on Darcy-Forchheimer flow of bioconvective micropolar nanofluid between double disks with Cattaneo-Christov heat flux
    (Elsevier, 2023) Shahzad, Arfan; Imran, Muhammad; Tahir, Madeeha; Khan, Shan Ali; Akgul, Ali; Abdullaev, Sherzod; Park, Choonkil
    The topic of fluid flow through disks is important due to a broad range of its applications in industries, engineering, and scientific fields. The objective of the current article is to analyze the bioconvective micropolar nanofluid flow between the coaxial, parallel, and radially stretching dou-ble disks in the occurrence of gyrotactic motile microorganisms with convective thermal boundary conditions. Darcy-Forchheimer medium is considered between the double disks that allow the flow horizontally with additional effects of porosity and friction. The flow is also considered under the impacts of thermal conductivity and thermal radiations. The influence of gyrotactic microorganisms is accommodated through the bioconvection, which increases the strength of thermal transporta-tion. Furthermore, the Cattaneo-Christov heat flux theory is also accounted. The flow model is trans moved into a system of ordinary differential equations (ODEs) utilizing appropriate similarity transformation functions. The bvp4c technique has been used to solve the transformed flow model. The implication of some prominent physical and bioconvection parameters on velocities, microro-tation, thermal field, volumetric concentration of nanoparticles, and microorganisms' fields are pre-sented through graphs and tabular ways. It is observed that the stretching ratio parameter of the disks accelerates the axial and micro rotational velocities of the nanofluid. In contrast, the stretch-ing Reynolds number slows down the radial velocity near the plane's center. The temperature pro-file goes high against the Brownian motion, thermal radiation, and thermal conductivity parameters, while an inverse trend has been observed for increasing magnitudes of Prandtl number. The nanoparticles concentration profile is upsurged against the thermophoresis parameter. The density profile of gyrotactic motile microorganisms is de-escalated by the Peclet number and the bioconvection Lewis number. Micropolar parameters cause an increase of couple stresses and a decrement in shear stresses. A comparison with published work is provided under certain limita-tions to test the validity of numerical scheme accuracy. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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    Lyapunov stability and wave analysis of Covid-19 omicron variant of real data with fractional
    (Elsevier, 2022) Xu, Changjin; Farman, Muhammad; Hasan, Ali; Akgul, Ali; Zakarya, Mohammed; Albalawi, Wedad; Park, Choonkil
    The fractional derivative is an advanced category of mathematics for real-life problems. This work focus on the investigation of 2nd wave of the Corona virus in India. We develop a time fractional order COVID-19 model with effects of the disease which consist of a system of fractional differential equations. The fractional-order COVID-19 model is investigated with AtanganaBaleanu-Caputo fractional derivative. Also, the deterministic mathematical model for the Omicron effect is investigated with different fractional parameters. The fractional-order system is analyzed qualitatively as well as verified sensitivity analysis. Fixed point theory is used to prove the existence and uniqueness of the fractional-order model. Analyzed the model locally as well as globally using Lyapunov first and second derivative. Boundedness and positive unique solutions are verified for the fractional-order model of infection of disease. The concept of fixed point theory is used to interrogate the problem and confine the solution. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease on society. Simulation has been made to understand the behavior of the virus.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).