Discrete Hahn polynomials for numerical solution of two-dimensional variable-order fractional Rayleigh–Stokes problem

Salehi, Farideh; Saeedi, Habibollah; Moghadam, M. M.

doi:10.1007/s40314-018-0631-5

Cited by 25 publications

(9 citation statements)

References 49 publications

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“…As a matter of fact, there have been lots of works devoted to finding numerical methods for solving Rayleigh-Stokes problem, see e.g. [1,2,3,4,12,16]. Regarding analytic representation for solution of this problem in linear form, we refer to [7,8,13,15,17,18].…”

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confidence: 99%

Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

Lân¹

2022

EECT

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We study the generalized Rayleigh-Stokes problem involving a fractional derivative and nonlinear perturbation. Our aim is to analyze some sufficient conditions ensuring the global solvability, regularity and asymptotic stability of solutions. In particular, if the nonlinearity is Lipschitzian then the mild solution of the mentioned problem becomes a classical one and its convergence to equilibrium point is proved.

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confidence: 99%

Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

Lân¹

2022

EECT

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“…That's because, in many applied systems, commonly available derivative information appears as a fractional order instead of integer order derivative. This holds true in a variety of scientific fields such as physics Yue et al (2018), Sayevand et al (2018), engineering problems Farideh and Habibollah (2018), finance Raberto et al (2002) and system control Kilbas et al (2006). Also, presented fractional HB interpolation in this paper can be considered to solve fractional differential equations numerically, regarding that most of the fractional differential equations do not have exact analytical solutions.…”

Section: Introductionmentioning

confidence: 97%

The Role of Hilbert–Schmidt SVD basis in Hermite–Birkhoff interpolation in fractional sense

2019

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The Hermite-Birkhoff (HB) interpolation is an extension of polynomial interpolation that appears when observation gives operational information. Additional capabilities in HB interpolation by considering fractional operators are created, as it occur in many applied systems. Due to the nice properties in kernel-based approximation, we intend to apply it to solve the HB interpolation in the fractional sense. We show the standard basis in kernel-based approximation is often insufficient for computing a stable solution in fractional HB interpolation. Because of the inherent ill-condition of kernel-based methods, we investigate the fractional HB interpolation using alternate Hilbert-Schmidt SVD (HS-SVD) bases, since it provides a linear transformation which can be applied analytically, and therefore, is able to remove a significant portion of the ill-conditioning. Also, the convergence and stability of the fractional HB interpolation using HS-SVD method are discussed. Numerical results show that in solving fractional HB interpolation, although the standard basis for many positive definite kernels is ill-conditioned in the flat limit, the HS-SVD basis solves the existing problem.

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“…In recent years, discrete polynomials have been extensively applied for solving diverse problems. For instances, see [39][40][41][42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

An accurate approach based on the orthonormal shifted discrete Legendre polynomials for variable-order fractional Sobolev equation

Heydari

Atangana

2021

Adv Differ Equ

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This paper applies the Heydari–Hosseininia nonsingular fractional derivative for defining a variable-order fractional version of the Sobolev equation. The orthonormal shifted discrete Legendre polynomials, as an appropriate family of basis functions, are employed to generate an operational matrix method for this equation. A new fractional operational matrix related to these polynomials is extracted and employed to construct the presented method. Using this approach, an algebraic system of equations is obtained instead of the original variable-order equation. The numerical solution of this system can be found easily. Some numerical examples are provided for verifying the accuracy of the generated approach.

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Discrete Hahn polynomials for numerical solution of two-dimensional variable-order fractional Rayleigh–Stokes problem

Cited by 25 publications

References 49 publications

Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

The Role of Hilbert–Schmidt SVD basis in Hermite–Birkhoff interpolation in fractional sense

An accurate approach based on the orthonormal shifted discrete Legendre polynomials for variable-order fractional Sobolev equation

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