Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

Wang, Yihong; Wu, Guo–Cheng; Băleanu, Dumitru

doi:10.2478/s11534-013-0207-3

Cited by 4 publications

(3 citation statements)

References 27 publications

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“…Some versions of the predictor-corrector variational iteration method for the solution of integral equations of fractional order were studied in [20] and [21].…”

Section: Introductionmentioning

confidence: 99%

A predictor-corrector iterative method for solving linear least squares problems and perturbation error analysis

Buranay

Iyikal

2019

J Inequal Appl

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The motivation of the present work concerns two objectives. Firstly, a predictor-corrector iterative method of convergence order p = 45 requiring 10 matrix by matrix multiplications per iteration is proposed for computing the Moore-Penrose inverse of a nonzero matrix of rank = r. Convergence and a priori error analysis of the proposed method are given. Secondly, the numerical solution to the general linear least squares problems by an algorithm using the proposed method and the perturbation error analysis are provided. Furthermore, experiments are conducted on the ill-posed problem of one-dimensional image restoration and on some test problems from Harwell-Boeing collection. Obtained numerical results show the applicability, stability, and the estimated order of convergence of the proposed method.

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“…Some versions of the predictor-corrector variational iteration method for the solution of integral equations of fractional order were studied in [20] and [21].…”

Section: Introductionmentioning

confidence: 99%

A predictor-corrector iterative method for solving linear least squares problems and perturbation error analysis

Buranay

Iyikal

2019

J Inequal Appl

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“…Especially, it should be pointed that Wu and Dumitru firstly suggest a universal way to identify the multiplier by implementing Laplace transform. The way is proved to be a simple but effective approach and used in many problems [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

“…In the paper, aiming at solving the FFW equation, we use the fractional iteration method (FVIM) with the Lagrange multiplier determined by the way in [32][33][34][35]. Besides, we use undetermined coefficient method for solving the nonlinear FFW equation based on Generalized Taylor formula.…”

Section: Introductionmentioning

confidence: 99%

Fractional Variational Iteration Method for Fractional Fornberg-Whitham Equation and Comparison with the Undetermined Coefficient Method

Bao

Deng²

2015

BJMCS

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The paper presents two methods for solving the fractional Fornberg-Whitham (FFW) equation. Based on the peaked solutions of FW equation, suppose the solution's variable-separated form, and the FFW equation is transformed into a constant fractional differential equation (FDE). To solve the transformed equation, first, the fractional variational iteration method (FVIM) is used. Secondly, the undetermined coefficient method is used to expand the solution of the constant FDE. The expansion is based on the Generalized Taylor formula. Also the solutions are yielded for FFW. It should be pointed out that two cases of the order of fractional derivative between 1 and 2 and that between 0 and 1 are discussed respectively for the transformed FDE. Last, we give two numerical examples by using the two presented methods. The results show that the results agree well by both two proposed methods, and the two methods are high efficient in solving FFW.

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Some Analytical Techniques in Fractional Calculus: Realities and Challenges

Băleanu

Duan

2013

Discontinuity and Complexity in Nonlinear Physical Systems

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Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

Cited by 4 publications

References 27 publications

A predictor-corrector iterative method for solving linear least squares problems and perturbation error analysis

A predictor-corrector iterative method for solving linear least squares problems and perturbation error analysis

Fractional Variational Iteration Method for Fractional Fornberg-Whitham Equation and Comparison with the Undetermined Coefficient Method

Some Analytical Techniques in Fractional Calculus: Realities and Challenges

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