Solving Fredholm integro–differential equations using reproducing kernel Hilbert space method

Arqub, Omar Abu; Al‐Smadi, Mohammed; Shawagfeh, Nabil

doi:10.1016/j.amc.2013.03.006

Cited by 119 publications

(82 citation statements)

References 24 publications

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“…For any two arbitrary fuzzy vectorsC ] ,D ] ∈ (F(R)) , the definition of algebraic operations between fuzzy-valued functions can be expressed, based on the parametric representation (8), as…”

Section: Remark 8 By Definitions 5 and 7 The Convexity Of Fuzzyvalumentioning

confidence: 99%

“…Therefore, in this paper, the portfolio selection problem under fuzzy environment based on the constrained fuzzy optimization problem is going to be studied. Many modern computing methodologies can be seen for various fuzzy systems, for example, [8][9][10][11][12][13][14]. It is also worth mentioning that there are several results associated with parametric representations of fuzzy numbers [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach

Fard

Ramezanzadeh

2017

Complexity

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Fuzzy portfolio selection problem is a major issue in the financial field and a special case of constrained fuzzy-valued optimization problems (CFOPs). In this respect, the present paper aims to investigate the CFOP with regard to the features of the parametric representation of fuzzy numbers named as convex constraint function (CCF) which is proposed by Chalco-Cano et al. in 2014. Furthermore, relying on this parametric representation, some proper conditions are provided for the existence of solutions to a CFOP. To this end, by the increasing representation of CCF, the main problem is converted to a parametric multiobjective programming problem and some solution concepts from a similar framework in the multiobjective programming are proposed for the CFOP. Eventually to illustrate the proposed results, the fuzzy portfolio selection problem is discussed.

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Section: Remark 8 By Definitions 5 and 7 The Convexity Of Fuzzyvalumentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach

Fard

Ramezanzadeh

2017

Complexity

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“…Examples of these methods are the Adomian decomposition method (ADM) Hosseinzadeh et al, 2017), the variational iteration method (Akter and Chowdhury, 2017;Wazwaz, 2015;Glowinski, 2015;Ghorbani and Bakherad, 2017), the pseudospectral method (Bhrawy et al, 2015;Wei et al, 2017;Borluk and Muslu, 2015) and the reproducing kernel Hilbert space method (Arqub et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Improvement of the homotopy perturbation method to nonlinear problems

Alzaidi¹,

Alderremy²

2018

Int. J. Phys. Sci.

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This paper proposes an effective improvement of the homotopy perturbation method (HPM) by using Jacobi and He's polynomials to solve some nonlinear ordinary differential equations. With this method, the source terms of ordinary differential equations can be expanded in series of shifted Jacobi polynomials. Numerical results are given in this paper to illustrate the reliability of this method with nonlinear ordinary differential equations.

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“…As a result, the solution of such equations can be approximated with a large variety of analytical numerical methods. Among these, homotopy perturbation method Odibat and Momani, 2008), variational iteration method (Odibat and Momani, 2006;Abbasbandy, 2007;Molliq et al, 2009), homotopy analysis method (Song and Zhang, 2007;Hashim et al, 2009;El-Ajou et al, 2010;Arqup and El-Ajou, 2013), transform methods (Arıkoğlu and Özkol, 2007;Oturanç et al, 2008;Ertürk and Momani, 2008;Momani et al, 2014) and other methods (Schneider, 1996;Arqub et al, 2012;Al-Smadi et al, 2013;Arqub et al, 2013;Arqub et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

An Expansion Iterative Technique for Handling Fractional Differential Equations Using Fractional Power Series Scheme

Abu-Gdairi¹,

Al‐Smadi²,

Gumah³

2015

Journal of Mathematics and Statistics

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In this study, we present a new analytical numerical technique for solving a class of time Fractional Differential Equations (FDEs) with variable coefficients based on the generalized Taylor series formula in the Caputo sense. This method provided the solution in the form of a rapidly convergent power series under a multiple fractional differentiability with easily computable components. An efficacious experiment is given to guarantee the procedure, to illustrate the theoretical statements of the present technique and to show its potentiality, generality and superiority for solving wide range of FDEs. The results reveal that the method is easy to implement, very effective, fully compatible with the complexity of such problems, straightforward and simple.

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Solving Fredholm integro–differential equations using reproducing kernel Hilbert space method

Cited by 119 publications

References 24 publications

On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach

On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach

Improvement of the homotopy perturbation method to nonlinear problems

An Expansion Iterative Technique for Handling Fractional Differential Equations Using Fractional Power Series Scheme

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