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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Previous articles were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence, and they are hosted by MDPI on mdpi.com as a courtesy and upon agreement with Association for Scientific Research (ASR).
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Article

The Approximate Solution of High-Order Linear Fractional Differential Equations with Variable Coefficients in Terms of Generalized Taylor Polynomials

by
Yıldıray Keskin
,
Onur Karaoğlu
and
Sema Servi
*
Galip OTURANÇ Department of Mathematics, Science Faculty, Selçuk University, Konya 42075, Turkey
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2011, 16(3), 617-629; https://doi.org/10.3390/mca16030617
Published: 1 December 2011
Versions Notes

Abstract

In this paper, we have developed a new method called Generalized Taylor collocation method (GTCM), which is based on the Taylor collocation method, to give approximate solution of linear fractional differential equations with variable coefficients. Using the collocation points, this method transforms fractional differential equation to a matrix equation which corresponds to a system of linear algebraic equations with unknown Generalized Taylor coefficients. Generally, the method is based on computing the Generalized Taylor coefficients by means of the collocation points. This method does not require any intensive computation. Moreover, It is easy to write computer codes in any symbolic language. Hence, the proposed method can be used as effective alternative method for obtaining analytic and approximate solutions for fractional differential equations. The effectiveness of the proposed method is illustrated with some examples. The results show that the method is very effective and convenient in predicting the solutions of such problems.
Keywords: Fractional differential equation; Taylor collocation method; Adomian decomposition method; Homotopy perturbation method; Variational iteration method; Fractional differential transformation method Fractional differential equation; Taylor collocation method; Adomian decomposition method; Homotopy perturbation method; Variational iteration method; Fractional differential transformation method

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MDPI and ACS Style

Keskin, Y.; Karaoğlu, O.; Servi, S. The Approximate Solution of High-Order Linear Fractional Differential Equations with Variable Coefficients in Terms of Generalized Taylor Polynomials. Math. Comput. Appl. 2011, 16, 617-629. https://doi.org/10.3390/mca16030617

AMA Style

Keskin Y, Karaoğlu O, Servi S. The Approximate Solution of High-Order Linear Fractional Differential Equations with Variable Coefficients in Terms of Generalized Taylor Polynomials. Mathematical and Computational Applications. 2011; 16(3):617-629. https://doi.org/10.3390/mca16030617

Chicago/Turabian Style

Keskin, Yıldıray, Onur Karaoğlu, and Sema Servi. 2011. "The Approximate Solution of High-Order Linear Fractional Differential Equations with Variable Coefficients in Terms of Generalized Taylor Polynomials" Mathematical and Computational Applications 16, no. 3: 617-629. https://doi.org/10.3390/mca16030617

APA Style

Keskin, Y., Karaoğlu, O., & Servi, S. (2011). The Approximate Solution of High-Order Linear Fractional Differential Equations with Variable Coefficients in Terms of Generalized Taylor Polynomials. Mathematical and Computational Applications, 16(3), 617-629. https://doi.org/10.3390/mca16030617

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