Genocchi Wavelet-like Operational Matrix and its Application for Solving Non-linear Fractional Differential Equations

Isah, Abdulnasir; Phang, Chang

doi:10.1515/phys-2016-0050

Cited by 27 publications

(12 citation statements)

References 28 publications

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“…However, this family of Genocchi polynomials in the interval of [0, h ) (what we called Genocchi wavelet basis) that inherit the advantages of utilizing wavelets. For more information, see other works …”

Section: Gwfs and Their Propertiesmentioning

confidence: 99%

On the applicability of Genocchi wavelet method for different kinds of fractional‐order differential equations with delay

Dehestani

Ordokhani

Razzaghi

2019

Numerical Linear Algebra App

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Summary A novel collocation method based on Genocchi wavelet is presented for the numerical solution of fractional differential equations and time‐fractional partial differential equations with delay. In this work, to achieve the approximate solution with height accuracy, we employed the operational matrix of integer derivative and the pseudo‐operational matrix of fractional derivative in Caputo sense. Also, based on Genocchi function properties, we presented delay and pantograph operational matrices of Genocchi wavelet functions (GWFs). Due to operational and pseudo‐operational matrices, the equations under this study can be turned into nonlinear algebraic equations with the unknown GWF coefficients. For illustrating the upper bound of error for the proposed method, we estimate the error in the sense of Sobolev space. In addition, to demonstrate the efficacy of the pseudo‐operational matrix of fractional derivative, we investigate the upper bound of error for the mentioned matrix. Finally, the algorithm based on the proposed approach is implemented for some numerical experiments to confirm accuracy and applicability.

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Section: Gwfs and Their Propertiesmentioning

confidence: 99%

On the applicability of Genocchi wavelet method for different kinds of fractional‐order differential equations with delay

Dehestani

Ordokhani

Razzaghi

2019

Numerical Linear Algebra App

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“…The Genocchi polynomials G n ( x ) and the Genocchi numbers g n , are an exponential generating function as follows:

\frac{2 t}{\exp t + 1} = true \sum_{n = 0}^{\infty} g_{n} \frac{t^{n}}{n!}, false| t false| < π,

\frac{2 t \exp x t}{\exp t + 1} = true \sum_{n = 0}^{\infty} G_{n} false(x false) \frac{t^{n}}{n!}, false| t false| < π .

…”

Section: Properties Of Genocchi Polynomialsmentioning

confidence: 99%

“…Here, we use a semi‐orthogonal polynomial which is called the Genocchi polynomials to obtain operational matrix for solving a class of FDEs where the fractional derivative is in Caputo‐Fabrizio sense. For approximating an arbitrary function, the Genocchi polynomials has advantages respect to other classical orthogonal polynomials …”

Section: Introductionmentioning

confidence: 99%

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Solving FDEs with Caputo‐Fabrizio derivative by operational matrix based on Genocchi polynomials

Roshan

Jafari

Băleanu

2018

Math Methods in App Sciences

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“…Kilbas et al [10] inclusively examined fractional differential and fractional integro-differential equations. In addition, numerical solutions of FDEs and the system of such equations have been presented using the Legendre polynomial operational matrix method [11], Bernstein operational matrix method [12], Genocchi operational matrix method [13], Jacobi operational matrix method [14], Chebyshev wavelet operational matrix method [15], polynomial least squares method (PLSM) [16], Legendre wavelet-like operational matrix method (LWPT) [17], and the Genocchi wavelet-like operational matrix method [18].…”

Section: Introductionmentioning

confidence: 99%

A New Operational Matrix of Fractional Derivatives to Solve Systems of Fractional Differential Equations via Legendre Wavelets

Seçer

Altun

2018

Mathematics

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This paper introduces a new numerical approach to solving a system of fractional differential equations (FDEs) using the Legendre wavelet operational matrix method (LWOMM). We first formulated the operational matrix of fractional derivatives in some special conditions using some notable characteristics of Legendre wavelets and shifted Legendre polynomials. Then, the system of fractional differential equations was transformed into a system of algebraic equations by using these operational matrices. At the end of this paper, several examples are presented to illustrate the effectivity and correctness of the proposed approach. Comparing the methodology with several recognized methods demonstrates that the advantages of the Legendre wavelet operational matrix method are its accuracy and the understandability of the calculations.

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Genocchi Wavelet-like Operational Matrix and its Application for Solving Non-linear Fractional Differential Equations

Cited by 27 publications

References 28 publications

On the applicability of Genocchi wavelet method for different kinds of fractional‐order differential equations with delay

On the applicability of Genocchi wavelet method for different kinds of fractional‐order differential equations with delay

Solving FDEs with Caputo‐Fabrizio derivative by operational matrix based on Genocchi polynomials

A New Operational Matrix of Fractional Derivatives to Solve Systems of Fractional Differential Equations via Legendre Wavelets

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