Fractional Variational Iteration Method and Its Application to Fractional Partial Differential Equation

Elbeleze, Asma Ali; Kılıçman, Adem; Taib, Bachok M.

doi:10.1155/2013/543848

Cited by 20 publications

(9 citation statements)

References 30 publications

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“…Many powerful numerical and analytical methods have been presented in literature on finance. Among them, homotopy perturbation method with Sumudu transform and Laplace transform [7][8][9], homotopy analysis method [10], fractional variational iteration method [11], variational iteration method with Sumudu transform, finite difference method [12] and fractional diffusion models [13,14] are relatively new approaches providing an analytical and numerical approximation to Black-Scholes option pricing equation. Methods described in [15,16] are the other numerical methods, used in order to solve dynamic problems in elastic media and generalized semi-infinite programming.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

Özdemir

Yavuz

2017

Acta Phys. Pol. A

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In this study, a new application of multivariate Padé approximation method has been used for solving European vanilla call option pricing problem. Padé polynomials have occurred for the fractional Black-Scholes equation, according to the relations of "smaller than", or "greater than", between stock price and exercise price of the option. Using these polynomials, we have applied the multivariate Padé approximation method to our fractional equation and we have calculated numerical solutions of fractional Black-Scholes equation for both of two situations. The obtained results show that the multivariate Padé approximation is a very quick and accurate method for fractional Black-Scholes equation. The fractional derivative is understood in the Caputo sense.

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Section: Introductionmentioning

confidence: 99%

Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

Özdemir

Yavuz

2017

Acta Phys. Pol. A

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“…According to standard VIM theory which was firstly proposed by He [28], we shall regenerate a corrected functional that allows us to construct an iteration formula in order to find fixed point of that formula. Based on this structure, the FVIM has already been presented and used by many authors [29][30][31][32].…”

Section: Process Of Fractional Vim (Fvim) For Fractional Pdementioning

confidence: 99%

Fractional variational iteration method for time-fractional non-linear functional partial differential equation having proportional delays

Dogan

Konuralp

2018

THERM SCI

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In this paper, time-fractional non-linear partial differential equation with proportional delays are solved by fractional variational iteration method taking into account modified Riemann-Liouville fractional derivative. The numerical solutions which are calculated by using this method are better than those obtained by homotopy perturbation method and differential transform method with same data set and approximation order. On the other hand, to improve the solutions obtained by fractional variational iteration method, residual error function is used. With this additional process, the resulting approximate solutions are getting closer to the exact solutions. The results obtained by taking into account different values of variables in the domain are supported by compared tables and graphics in detail.

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“…There are many methods for finding the approximate solutions for nonlinear FDEs such as variation iteration method, homotopy perturbation method, Adomian decomposition method, differential transform method, and homotopy analysis method [10][11][12][13][14][15][16][17][18][19][20]. However, an effective and general method for solving these types of equations cannot be found.…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave Solutions of Nonlinear Conformable Time-Fractional Boussinesq Equations

2019

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In this paper, the (G G)-expansion method based on conformable fractional derivative is proposed to solve time fractional partial differential equations in mathematical physics. To illustrate the validity of this method, we solve the Boussinesq equation, coupled time-fractional Boussinesq equations and a variety of exact solutions for them are successfully established. With the help of Maple software, three-dimensional solution graphs are presented.

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Fractional Variational Iteration Method and Its Application to Fractional Partial Differential Equation

Cited by 20 publications

References 30 publications

Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

Fractional variational iteration method for time-fractional non-linear functional partial differential equation having proportional delays

Solitary Wave Solutions of Nonlinear Conformable Time-Fractional Boussinesq Equations

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