Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model

Nikan, O.; Avazzadeh, Z.; Machado, J. A. Tenreiro

doi:10.1016/j.apm.2021.07.025

Cited by 49 publications

(26 citation statements)

References 52 publications

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“…The third definition is a function of integration variable x; however, when using this definition in (21), it should be understood that this is not part of the integration. Only after the fractional derivative is obtained can α = α(x) be used, as indicated by (19) or (20), i.e., this is a delayed order. The first case where α = α 0 has always been dealt with in the literature.…”

Section: Derivative Of Functions To Functional-ordermentioning

confidence: 99%

Dualities and Asymptotic Mixtures Using Functional-Order Differentiation

Alexopoulos

2022

AppliedMath

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New definitions for fractional integro-differential operators are presented and referred to as delayed fractional operators. It is shown that delayed fractional derivatives give rise to the notion of functional order differentiation. Functional differentiation can be used to establish dualities and asymptotic mixtures between unrelated theories, something that conventional fractional or integer operators cannot do. In this paper, dualities and asymptotic mixtures are established between arbitrary functions, probability densities, the Gibbs–Shannon entropy and Hellinger distance, as well as higher-dimensional particle geometries in quantum mechanics.

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Section: Derivative Of Functions To Functional-ordermentioning

confidence: 99%

Dualities and Asymptotic Mixtures Using Functional-Order Differentiation

Alexopoulos

2022

AppliedMath

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“…In the last decade, FC has received considerable attention in a variety of scientific areas [3][4][5][6]. In most cases, it is difficult to compute an explicit solution to fractional differential equations, which has attracted researchers to look for accurate and efficient numerical approaches for solving these Equations [7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Numerical Approximation of the Fractional Rayleigh–Stokes Problem Arising in a Generalised Maxwell Fluid

et al. 2022

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This paper presents a numerical technique to approximate the Rayleigh–Stokes model for a generalised Maxwell fluid formulated in the Riemann–Liouville sense. The proposed method consists of two stages. First, the time discretization of the problem is accomplished by using the finite difference. Second, the space discretization is obtained by means of the predictor–corrector method. The unconditional stability result and convergence analysis are analysed theoretically. Numerical examples are provided to verify the feasibility and accuracy of the proposed method.

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“…Nonetheless, global RBF (GRBF) approximations result in ill-conditioned and full matrices, which makes them unsuitable for large problems. Consequently, local strategies, such as the RBF partition of unity (RBF-PU) [23,[36][37][38][39][40][41] and the RBF-generated finite-difference (RBF-FD) approaches [42][43][44][45], are currently under development.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks

et al. 2022

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This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of the two-dimensional time-fractional Sobolev equation. The model is formulated with the Caputo fractional derivative. The method uses the RBF to approximate the spatial operator, and a finite-difference algorithm as the time-stepping approach for the solution in time. The stability of the technique is examined by using the matrix method. Finally, two numerical examples are given to verify the numerical performance and efficiency of the method.

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Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model

Cited by 49 publications

References 52 publications

Dualities and Asymptotic Mixtures Using Functional-Order Differentiation

Dualities and Asymptotic Mixtures Using Functional-Order Differentiation

Numerical Approximation of the Fractional Rayleigh–Stokes Problem Arising in a Generalised Maxwell Fluid

Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks

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