An initial and boundary value problem of fractional Jeffreys’ fluid in a porous half space

Guo, Xiaoyi; Fu, Zunwei

doi:10.1016/j.camwa.2015.11.020

Cited by 22 publications

(6 citation statements)

References 14 publications

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“…In [21], Zakarya et al provided novel generalizations by considering the generalized conformable fractional integrals for reverse Copson's type inequalities on time scales. For some other applications of fractional calculus, the reader is referred to [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. This paper deals with the following sub-diffusion model with a changing-sign perturbation.…”

Section: Introductionmentioning

confidence: 99%

A Singular Tempered Sub-Diffusion Fractional Equation with Changing-Sign Perturbation

Zhang,

Chen,

et al. 2024

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In this paper, we establish some new results on the existence of positive solutions for a singular tempered sub-diffusion fractional equation involving a changing-sign perturbation and a lower-order sub-diffusion term of the unknown function. By employing multiple transformations, we transform the changing-sign singular perturbation problem to a positive problem, then establish some sufficient conditions for the existence of positive solutions of the problem. The asymptotic properties of solutions are also derived. In deriving the results, we only require that the singular perturbation term satisfies the Carathéodory condition, which means that the disturbance influence is significant and may even achieve negative infinity near some time singular points.

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Section: Introductionmentioning

confidence: 99%

A Singular Tempered Sub-Diffusion Fractional Equation with Changing-Sign Perturbation

Zhang,

Chen,

et al. 2024

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“…Liu et al 49 have presented semi-analytical solutions of oscillating EOF of linear viscoelastic fluids described as the Jeffrey fluid model through slit microchannels using the method of separation of variables. Based on the modified Darcys law, Guo and Fu 50 presented the exact analytical solution for fractional Jeffrey fluids into a porous half space using the discrete Laplace transform and Foxs H-function. Peralta et al 51 have carried out an analytical study for mass transfer of an electrically neutral solute in a concentric-annular microtube controlled by an oscillatory EOF of a fluid that behaves like a Maxwell fluid.…”

Section: Introductionmentioning

confidence: 99%

Impact of hydrodynamics and rheology of the ion partitioning effect on electrokinetic flow through a soft annulus with a retentive and absorptive wall

2023

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“…Boundary value problems arise everywhere in engineering (Khan, 2018; Bilige and Han, 2018; Yadav et al , 2019; Abu Arqub, 2018; Tian and He, 2018; Qiu, 2018; Karakas, 2018) and serve as “numerical building blocks” for many computational fluid dynamics software. More and more evidences have been reported that an unsmooth boundary or a porous medium can greatly affect the mass, energy and charge transfer through the boundary (Guo and Fu, 2019; Sivasankaran et al , 2019; Genbach et al , 2019; He et al , 2019). A suitable boundary morphology can result in an extremely fast convection–diffusion process (He, 2019a).…”

Section: Introductionmentioning

confidence: 99%

A short review on analytical methods for a fully fourth-order nonlinear integral boundary value problem with fractal derivatives

2020

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Purpose This paper aims to review some effective methods for fully fourth-order nonlinear integral boundary value problems with fractal derivatives. Design/methodology/approach Boundary value problems arise everywhere in engineering, hence two-scale thermodynamics and fractal calculus have been introduced. Some analytical methods are reviewed, mainly including the variational iteration method, the Ritz method, the homotopy perturbation method, the variational principle and the Taylor series method. An example is given to show the simple solution process and the high accuracy of the solution. Findings An elemental and heuristic explanation of fractal calculus is given, and the main solution process and merits of each reviewed method are elucidated. The fractal boundary value problem in a fractal space can be approximately converted into a classical one by the two-scale transform. Originality/value This paper can be served as a paradigm for various practical applications.

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An initial and boundary value problem of fractional Jeffreys’ fluid in a porous half space

Cited by 22 publications

References 14 publications

A Singular Tempered Sub-Diffusion Fractional Equation with Changing-Sign Perturbation

A Singular Tempered Sub-Diffusion Fractional Equation with Changing-Sign Perturbation

Impact of hydrodynamics and rheology of the ion partitioning effect on electrokinetic flow through a soft annulus with a retentive and absorptive wall

A short review on analytical methods for a fully fourth-order nonlinear integral boundary value problem with fractal derivatives

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