Efficient numerical methods for Riesz space-fractional diffusion equations with fractional Neumann boundary conditions

Xie, Changping; Fang, Shaomei

doi:10.1016/j.apnum.2022.01.008

Cited by 4 publications

(1 citation statement)

References 37 publications

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“…Anomalous sub diffusion wherein the spread of particles occurs slower than the classical diffusion was numerically solved via compact finite differences in space and Grn¨wald–Letnikov scheme in fractional time in Al-Shibani et al (2013). A few more such recent attempts are variational iteration method (Ates and Yıldırım, 2010), operational Tau method (Vanani and Aminataei, 2012), homotopy perturbation method (Liu and Dong, 2015), reproducing kernel (Arqub, 2018), H2 matrix representation (Boukaram et al , 2020), nonpolynomial spline functions (Hasan and Salim, 2021), Legendre spectral method (Liu and Lu, 2021), Sinc and B-Spline interpolation (Adibmanesha and Rashidiniab, 2021), Chebyshev wavelets (Dincel and Polat, 2021), meshless methods (Nikan et al , 2021; Bavi et al , 2022), Crank–Nicholson method (Xie and Fang, 2022), neural network method with shifted Legendre orthogonal polynomials (Qu et al , 2022), compact implicit difference method (Ali et al , 2022), finite volume method (Fang et al , 2022) and boundary integral equation method (Yao and Wang, 2022).…”

Section: Introductionmentioning

confidence: 99%

Transient and passage to steady state in fluid flow and heat transfer within fractional models

Türkyılmazoğlu

2022

HFF

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Purpose The classical integer derivative diffusionmodels for fluid flow within a channel of parallel walls, for heat transfer within a rectangular fin and for impulsive acceleration of a quiescent Newtonian fluid within a circular pipe are initially generalized by introducing fractional derivatives. The purpose of this paper is to represent solutions as steady and transient parts. Afterward, making use of separation of variables, a fractional Sturm–Liouville eigenvalue task is posed whose eigenvalues and eigenfunctions enable us to write down the transient solution in the Fourier series involving also Mittag–Leffler function. An alternative solution based on the Laplace transform method is also provided. Design/methodology/approach In this work, an analytical formulation is presented concerning the transient and passage to steady state in fluid flow and heat transfer within the diffusion fractional models. Findings From the closed-form solutions, it is clear to visualize the start-up process of physical diffusion phenomena in fractional order models. In particular, impacts of fractional derivative in different time regimes are clarified, namely, the early time zone of acceleration, the transition zone and the late time regime of deceleration. Originality/value With the newly developing field of fractional calculus, the classical heat and mass transfer analysis has been modified to account for the fractional order derivative concept.

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