Solving systems of linear Fredholm integro-differential equations with Fibonacci polynomials

Mirzaee, Farshid; Hoseini, Seyede Fatemeh

doi:10.1016/j.asej.2013.09.002

Cited by 28 publications

(14 citation statements)

References 28 publications

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“…In recent years, some authors use the well-known polynomials and numbers in the applications of ordinary and fractional differential equations and difference equations (for example [20][21][22][23]). Therefore, our new families of three variables polynomials could been used for future works of some application areas such as mathematical modelling, physics, engineering, and applied sciences.…”

Section: Discussionmentioning

confidence: 99%

New Families of Three-Variable Polynomials Coupled with Well-Known Polynomials and Numbers

et al. 2019

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In this paper, firstly the definitions of the families of three-variable polynomials with the new generalized polynomials related to the generating functions of the famous polynomials and numbers in literature are given. Then, the explicit representation and partial differential equations for new polynomials are derived. The special cases of our polynomials are given in tables. In the last section, the interesting applications of these polynomials are found.

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Section: Discussionmentioning

confidence: 99%

New Families of Three-Variable Polynomials Coupled with Well-Known Polynomials and Numbers

et al. 2019

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“…Mirzaee et al in [12,13] used this method for solving systems of linear Fredholm integrodifferential equations and Fredholm-Volterra integral equations in two-dimensional spaces. Also, Koc et al in [8] for solving boundary value problems and Kurt et al in [9] solved high order linear Fredholm integro-differential-difference equations by using this method.…”

Section: Introductionmentioning

confidence: 98%

Fibonacci-regularization method for solving Cauchy integral equations of the first kind

Araghi

Noeiaghdam

2017

Ain Shams Engineering Journal

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In this paper, a novel scheme is proposed to solve the first kind Cauchy integral equation over a finite interval. For this purpose, the regularization method is considered. Then, the collocation method with Fibonacci base function is applied to solve the obtained second kind singular integral equation. Also, the error estimate of the proposed scheme is discussed. Finally, some sample Cauchy integral equations stem from the theory of airfoils in fluid mechanics are presented and solved to illustrate the importance and applicability of the given algorithm. The tables in the examples show the efficiency of the method. Ó 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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“…Çakmak 15 adapted the FPs for solving Lane-Emden type equations. These polynomials are used in Mirzaee and Hoseini 16 to solve systems of integro-differential equations. Mirzaee and Hoseini 17 used the FPs for solving integral equations.…”

Section: Introductionmentioning

confidence: 99%

Fibonacci polynomials for the numerical solution of variable‐order space‐time fractional Burgers‐Huxley equation

Heydari

Avazzadeh

2021

Math Methods in App Sciences

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In this article, the variable-order (VO) space-time fractional version of the Burgers-Huxley equation is introduced with fractional differential operator of the Caputo type. The collocation technique based on the Fibonacci polynomials (FPs) is developed for finding the approximate solution of this equation.In order to implement the presented method, some novel operational matrices of derivative (including ordinary and fractional derivatives) are extracted for the FPs. Moreover, the roots of the Chebyshev polynomials of the first kind are chosen as the collocation points which reduce the equation to a system of algebraic equations more efficiency. Ultimately, we obtain the solution of the VO space-time fractional Burgers-Huxley equation in terms of the FPs. The devised method is validated by finding an error bound for the truncated series of the Fibonacci expansion in two dimensions. The accuracy of approximation is verified through various illustrative examples.

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Solving systems of linear Fredholm integro-differential equations with Fibonacci polynomials

Cited by 28 publications

References 28 publications

New Families of Three-Variable Polynomials Coupled with Well-Known Polynomials and Numbers

New Families of Three-Variable Polynomials Coupled with Well-Known Polynomials and Numbers

Fibonacci-regularization method for solving Cauchy integral equations of the first kind

Fibonacci polynomials for the numerical solution of variable‐order space‐time fractional Burgers‐Huxley equation

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