Spectral collocation method for linear fractional integro-differential equations

Ma, Xiaohua; Huang, Chengming

doi:10.1016/j.apm.2013.08.013

Cited by 100 publications

(48 citation statements)

References 27 publications

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“…Therefore, finding more accurate solutions using numerical schemes can be helpful. Some numerical algorithm for solving integrodifferential equation of fractional order can be summarized as follows: but not limited to; Adomian decomposition method [16,18,19], Laplace decomposition method [32], Taylor expansion method [9], least squares method [17] differential transform method [5,21], Spectral collocation method [14], Legendre wavelets method [24,26], Haar wavelets method [7], Chebyshev wavelets method [29,33,37], piecewise collocation methods [23,36], Chebyshev pseudo-spectral method [10,31], homotopy analysis method [1,35,38], homotopy perturbation method [6,20,25] and variational iteration method [6,20].…”

Section: Introductionmentioning

confidence: 99%

Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order

Alkan

Hatipoğlu

2017

Tbilisi Math. J.

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Section: Introductionmentioning

confidence: 99%

Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order

Alkan

Hatipoğlu

2017

Tbilisi Math. J.

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“…Furthermore, it is seen that many numerical methods have been given to evaluate fractional order integrals and the solution of fractional order differential equations [17][18][19][20][21][22][23][24][25]. As shown in the above mentioned works, the principal difficulty in evaluating fractional order integrals is how to deal with the weakly singular kernel.…”

Section: Ay (T) + B D α Y(t) + Cy(t) = F(t)mentioning

confidence: 99%

Approximate Solution of Bagley–Torvik Equations with Variable Coefficients and Three-point Boundary-value Conditions

Huang

Zhong

Guo

2015

Int. J. Appl. Comput. Math

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The fractional Bagley-Torvik equation with variable coefficients is investigated under three-point boundary-value conditions. By using the integration method, the considered problems are transformed into Fredholm integral equations of the second kind. It is found that when the fractional order is 1 < α < 2, the obtained Fredholm integral equation is with a weakly singular kernel. When the fractional order is 0 < α < 1, the given Fredholm integral equation is with a continuous kernel or a weakly singular kernel depending on the applied boundary-value conditions. The uniqueness of solution for the obtained Fredholm integral equation of the second kind with weakly singular kernel is addressed in continuous function spaces. A new numerical method is further proposed to solve Fredholm integral equations of the second kind with weakly singular kernels. The approximate solution is made and its convergence and error estimate are analyzed. Several numerical examples are computed to show the effectiveness of the solution procedures.

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“…Therefore, finding more accurate solutions using numerical schemes can be helpful. Some numerical algorithm for solving integrodifferential equation of fractional order can be summarized as follows, but not limited to; Adomian decomposition method [1, 2, 23], Taylor expansion method [3], differential transform method [4,5] and homotopy perturbation method [6,7], Spectral collocation method [14], Legendre wavelets method [13], Chebyshev wavelets method [15,29], piecewise collocation methods [20,21], Chebyshev pseudo-spectral method [24,28], homotopy analysis method [25,26], variational iteration method [27].…”

Section: Introductionmentioning

confidence: 99%

Kesirli mertebeden integro-diferansiyel denklemlerin çözümü için sayısal bir yöntem

Alkan¹

2017

SAÜ Fen Bilimleri Enstitüsü Dergisi

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In this study, sinc-collocation method is introduced for solving Volterra integro-differential equations of fractional order. Fractional derivative is described in the Caputo sense often used in fractional calculus. Obtained results are given to literature as two new theorems. Some numerical examples are presented to demonstrate the theoretical results.Keywords: Integro-differential equation, sinc-collocation method, Caputo fractional derivative. Kesirli mertebeden integro-diferansiyel denklemlerin çözümü için sayısal bir yöntem ÖZBu çalışmada, sinc sıralama yöntemi kesirli mertebeden Volterra integro-diferansiyel denklemleri yaklaşık olarak çözmek için geliştirilmiştir. Kesirli türev, kesirli analizde sıkça kullanılan Caputo anlamında tanımlanmıştır. Elde edilen sonuçlar iki yeni teorem ile verilmiştir. Bazı sayısal örnekleri teorik sonuçları göstermek için sunulmuştur.Anahtar kelimeler: Integro-diferansiyel denklem, sinc-sıralama yöntemi, Caputo kesirli türevi.

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Spectral collocation method for linear fractional integro-differential equations

Cited by 100 publications

References 27 publications

Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order

Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order

Approximate Solution of Bagley–Torvik Equations with Variable Coefficients and Three-point Boundary-value Conditions

Kesirli mertebeden integro-diferansiyel denklemlerin çözümü için sayısal bir yöntem

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