Analytical and numerical solutions of a two‐dimensional multi‐term time‐fractional Oldroyd‐B model

Zhang, Jinghua; Liu, Fawang; Anh, Vo

doi:10.1002/num.22327

Cited by 12 publications

(7 citation statements)

References 39 publications

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“…Feng et al [2,3] gave two implicit finite difference schemes using the L1 formula and proved the stability and convergence of the proposed schemes with the global convergence orders of O(τ +h 2 ) and O(τ min{3−γ,2−β} +h 2 ), respectively. Zhang et al [24] obtained analytical and numerical solutions of a two-dimensional multi-term time-fractional Oldroyd-B model. The convergence order of the numerical scheme is O(τ + h 2 1 + h 2 2 ).…”

Section: Introductionmentioning

confidence: 99%

Two novel difference schemes for the one-dimensional multi-term time fractional Oldroyd-B equation

Guan

2023

Preprint

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In this paper, two novel difference schemes, which are based on the order reduction technique together with the weighted and shifted Grünwald-Letnikov difference (WSGD) operator, are derived for the one-dimensional multi-term time fractional Oldroyd-B equation. Utilizing the discrete energy method, we proved that the schemes are unconditionally stable and convergent in the maximum norm with the global convergence orders O(τ2−β + h2) and O(τ2−β + h4), respectively. Finally, a numerical example is carried out to verify the theoretical results, showing that our schemes are efficient indeed and have higher accuracy compared with the existed methods.

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Section: Introductionmentioning

confidence: 99%

Two novel difference schemes for the one-dimensional multi-term time fractional Oldroyd-B equation

Guan

2023

Preprint

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“…Chen [18] studied analytical solution for the time-fractional telegraph equation by the separation of variables method (SVM). Zhang [19] obtained the analytical solution for a two-dimensional multi-term time-fractional Oldroyd-B equation on a rectangular domain by the SVM, based on the Caputo time-fractional derivative. Consequently, the purpose of this paper is to consider the fractional constitutive equation with the Caputo fractional derivative, and present the analytical solutions corresponding to the two types of unsteady unidirectional flows of a generalized Oldroyd-B fluid between two parallel plates.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions to Unsteady Unidirectional Flows of a Generalized Oldroyd-B Fuid

Wang¹,

Wang²

2022

Preprint

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For solving the fractional differential equations in computational fluid dynamics (CFD), it’s complicated and difficult by the Laplace and Fourier transforms. Based on the Caputo fractional derivative, the analytical solutions for unsteady unidirectional flows of a generalized Oldroyd-B fluid are deduced by the separation of variables method. Results show that the analytical solutions are given easily, and have good university. For some specific parameter values, the well-known analytical solutions for the generalized second grade fluid, the generalized Upper-Convected Maxwell (UCM) fluid as well as the ordinary Oldroyd-B fluid can be obtained.

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“…Zafar et al [41] contemplated an OBF for circular cylinders with nonintegerorder derivatives. Zhang et al [42] examined the analytical solutions for time-fractional OBF utilizing the definition of Caputo derivative. As of late, Riaz and Saeed [43] evaluated the conduct of MHD OBF under slip condition with the assistance of integer order, Caputo-Fabrizio, and Atangana-Baleanu fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

Functional Application of G-Functions of Lorenzo and Hartley on the Free Convection Flow of Oldroyd-B Fluid with Ordinary and Fractional Techniques

et al. 2021

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In this article, free convection flow of an Oldroyd-B fluid (OBF) through a vertical rectangular channel in the presence of heat generation or absorption subject to generalized boundary conditions is studied. The fractionalized mathematical model is established by Caputo time-fractional derivative through mechanical laws (generalized shear stress constitutive equation and generalized Fourier’s law). Closed form solutions for the velocity and temperature profiles are obtained via Laplace coupled with sine-Fourier transforms and have been embedded with regards to the special functions, namely, the generalized G-functions of Lorenzo and Hartley. Solutions of the known results from recently published work (Nehad et al. Chin. J. Phy., 65, (2020) 367–376) are recovered as limiting cases. Finally, the effects of fractional and various physical parameters are graphically underlined. Furthermore, a comparison between Oldroyd-B, Maxwell and viscous fluids (fractional and ordinary) is depicted. It is found that, for short time, ordinary fluids have greater velocity as compared to the fractional fluids.

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Analytical and numerical solutions of a two‐dimensional multi‐term time‐fractional Oldroyd‐B model

Cited by 12 publications

References 39 publications

Two novel difference schemes for the one-dimensional multi-term time fractional Oldroyd-B equation

Two novel difference schemes for the one-dimensional multi-term time fractional Oldroyd-B equation

Analytical Solutions to Unsteady Unidirectional Flows of a Generalized Oldroyd-B Fuid

Functional Application of G-Functions of Lorenzo and Hartley on the Free Convection Flow of Oldroyd-B Fluid with Ordinary and Fractional Techniques

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