Chebyshev–Gauss–Lobatto collocation method for variable-order time fractional generalized Hirota–Satsuma coupled KdV system

Heydari, M. H.; Avazzadeh, Z.

doi:10.1007/s00366-020-01125-5

Cited by 15 publications

(3 citation statements)

References 36 publications

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“…This is because of the simplicity of computing their fractional derivatives and integrals and the high accuracy of their approximation. So, during recent years, various numerical methods have been designed using the polynomial basis functions for different classes of fractional differential equations, for example, previous works 47‐49 …”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of variable‐order fractional Benjamin–Bona–Mahony–Burgers equation using a pseudo‐spectral method

Heydari

Razzaghi

Avazzadeh

2021

Math Methods in App Sciences

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This article introduces a new local variable‐order (VO) fractional differentiation called the VO conformable fractional derivative. This derivative is employed to define the VO time fractional Benjamin–Bona–Mahony–Burgers (BBMB) equation. A pseudo‐spectral algorithm using the Chebyshev cardinal functions (CCFs) is adopted to find a numerical solution for this equation. The presented method with the help of the CCFs derivative matrices (which are obtained in this research) turns problem solving into solving an algebraic system of equations. The proposed approach is applied on some test problems, and its accuracy is examined in terms of L∞ and L2 error norms. A numerical comparison is performed between the achieved results of the method with the results obtained from the cubic B‐spline method and the hybrid method generated using the quintic Hermite approach and the finite difference technique.

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Section: Introductionmentioning

confidence: 99%

Numerical investigation of variable‐order fractional Benjamin–Bona–Mahony–Burgers equation using a pseudo‐spectral method

Heydari

Razzaghi

Avazzadeh

2021

Math Methods in App Sciences

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“…Therefore, it is very important to propose approximation/numerical procedures to find numerical solutions for these problems. Some recent studies and numerical methods for V-O fractional functional equations can be observed in [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations

et al. 2020

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In this study, a wavelet method is developed to solve a system of nonlinear variable-order (V-O) fractional integral equations using the Chebyshev wavelets (CWs) and the Galerkin method. For this purpose, we derive a V-O fractional integration operational matrix (OM) for CWs and use it in our method. In the established scheme, we approximate the unknown functions by CWs with unknown coefficients and reduce the problem to an algebraic system. In this way, we simplify the computation of nonlinear terms by obtaining some new results for CWs. Finally, we demonstrate the applicability of the presented algorithm by solving a few numerical examples.

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“…So numerical schemes are unavoidable for solving this type of equations. The curious reader is advised to consult on previous studies 5‐9 to see several numerical techniques for such VO fractional functional equations.…”

Section: Introductionmentioning

confidence: 99%

A numerical method based on the Chebyshev cardinal functions for variable‐order fractional version of the fourth‐order 2D Kuramoto‐Sivashinsky equation

Hosseininia

Heydari

Hooshmandasl

et al. 2020

Math Methods in App Sciences

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In this article, the variable-order (VO) time fractional 2D Kuramoto-Sivashinsky equation is introduced, and a semidiscrete approach is presented through 2D Chebyshev cardinal functions (CCFs) for solving this equation. In the proposed method, we obtain a recurrent algorithm by using the finite difference method to approximate the VO fractional differentiation, the weighted finite difference method with parameter , and the approximation of the unknown function by the 2D CCFs. The differentiation operational matrices and the collocation technique are used to extract a linear system of algebraic equations which can be easily solved. The credibility of the developed method is examined on three numerical examples.

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Chebyshev–Gauss–Lobatto collocation method for variable-order time fractional generalized Hirota–Satsuma coupled KdV system

Cited by 15 publications

References 36 publications

Numerical investigation of variable‐order fractional Benjamin–Bona–Mahony–Burgers equation using a pseudo‐spectral method

Numerical investigation of variable‐order fractional Benjamin–Bona–Mahony–Burgers equation using a pseudo‐spectral method

Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations

A numerical method based on the Chebyshev cardinal functions for variable‐order fractional version of the fourth‐order 2D Kuramoto‐Sivashinsky equation

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