Anomalous convection diffusion and wave coupling transport of cells on comb frame with fractional Cattaneo–Christov flux

Liu, Lin; Zheng, Liancun; Liu, Fawang; Zhang, Xinxin

doi:10.1016/j.cnsns.2016.02.009

Cited by 61 publications

(22 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fractional derivatives, which are a generalization of classical derivatives have been extensively used in describing and solving integral equations, ordinary and partial differential equations in applied sciences such as fluid mechanics, diffusive transport, electrical networks, electrodynamics, nonlinear control theory, signal processing, nonlinear biological systems, astrophysics, among others [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Solís-Pérez

Gómez-Aguilar

Băleanu

et al. 2018

Entropy

View full text Add to dashboard Cite

This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and β-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and β-conformable attractors are provided to illustrate the effectiveness of the proposed method.

show abstract

Section: Introductionmentioning

confidence: 99%

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Solís-Pérez

Gómez-Aguilar

Băleanu

et al. 2018

Entropy

View full text Add to dashboard Cite

show abstract

“…The model, which is given by Equation (2.8), is then known as a generalized Oldroyd-B model. Research related to non-Newtonian fluid mechanics is of great realistic significance to industry [2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Liu

Anh

2019

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

In this paper, we consider a two‐dimensional multi‐term time‐fractional Oldroyd‐B equation on a rectangular domain. Its analytical solution is obtained by the method of separation of variables. We employ the finite difference method with a discretization of the Caputo time‐fractional derivative to obtain an implicit difference approximation for the equation. Stability and convergence of the approximation scheme are established in the L∞‐norm. Two examples are given to illustrate the theoretical analysis and analytical solution. The results indicate that the present numerical method is effective for this general two‐dimensional multi‐term time‐fractional Oldroyd‐B model.

show abstract

“…Christov [6] modified Cattaneo model [3] via insertion of upper-convected Oldroyd's derivative. Some researches elaborating flow subjected to Cattaneo-Christov (non-Fourier) heat flux are given in [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Significance of improved Fourier-Fick laws in non-linear convective micropolar material stratified flow with variable properties

et al. 2019

View full text Add to dashboard Cite

Present research article describes the effectiveness of improved Fourier-Fick fluxes and temperature-dependent conductivity on the 2-D, incompressible steady micropolar material flow over a stretchable surface. Non-linear mixed convection, double stratification and heat generation aspects are considered. The considered flow non-linear PDE are converted to ODE via appropriate transformations. Through implementation of homotopy method the obtain system is solved for series solutions. The effects of pertinent parameters are discussed through graphical sketch. Skin friction coefficient (drag force) is calculated. Main findings are pointed out.

show abstract

Anomalous convection diffusion and wave coupling transport of cells on comb frame with fractional Cattaneo–Christov flux

Cited by 61 publications

References 31 publications

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

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

Significance of improved Fourier-Fick laws in non-linear convective micropolar material stratified flow with variable properties

Contact Info

Product

Resources

About