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Inverse Laplace transform method for multiple solutions of the fractional Sturm-Liouville problems | ||
| Computational Methods for Differential Equations | ||
| مقاله 8، دوره 2، شماره 1، فروردین 2014، صفحه 56-61 اصل مقاله (220.64 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Farhad Dastmalchi Saei* ؛ Sadegh Abbasi؛ Zhila Mirzayi | ||
| Tabriz Azad University | ||
| چکیده | ||
| In this paper, inverse Laplace transform method is applied to analytical solution of the fractional Sturm-Liouville problems. The method introduces a powerful tool for solving the eigenvalues of the fractional Sturm-Liouville problems. The results how that the simplicity and efficiency of this method. | ||
| کلیدواژهها | ||
| Laplace transform؛ Fractional Sturm-Liouville problem؛ Caputo's fractional derivative؛ eigenvalue | ||
| مراجع | ||
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[1] S. Abbasbandy, A. Shirzadi, Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems, Numer Algor 54 (2010), 521-532. [2] Q.M. Al-Mdallal, An efficient method for solving fractional Sturm-Liouville problems, Chaos Soluitions Fractals 40 (2009), 138-189. [3] A.M. Cohen, Numerical method for Laplace transform inversion, springer, New York, 2007.
[4] G.M. Mittag-Leffler, Sur la nouvelle fonction Eα(x), Comptes Rendusdel Academie des Sciences SerieII Paris 137 (1903), 554-558. [5] P. Humbert and R.P. Agarwal, Surlafonction de Mittag-Leffler et quelques-unes de ses generalisations, Bulletin des Sciences Mathematiques SeriesII 77 (1953), 180-185. [6] K.B. Oldham and j. Spanier, The Fractional Calculus, Academic, New York, 1974.
[7] K.S. Miller and B Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley and Sons, New York, 1993. [8] I. Podlubny, Fractional differential equations, Academic, New York, 1999.
[9] SG. Samko, AA. Kilbas, and OI. Marichev, Fractional integrals and derivatives, Berlin: Gorden and Breach, 1993. [10] H. Sheng, Y. Li, and Y. Chen, Application of numerical inverse Laplace transform algorithms in fractional calculus, Journal of the Franklin Institute 348 (2011), 315-330. | ||
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