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Sumudu transform iteration method for fractional diffusion-wave equations | ||
| Journal of Hyperstructures | ||
| دوره 4، شماره 2، اسفند 2015، صفحه 156-159 اصل مقاله (1.81 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2015.2606 | ||
| نویسندگان | ||
| Khosro Sayevand* 1؛ Kazem Pichaghchi2 | ||
| 1Faculty of Mathematical Sciences, University of Malayer, P. O. Box 65718-18164, Malayer, Iran | ||
| 2Faculty of Mathematical Sciences, Malayer University, P. O. Box 16846-13114 Malayer, Iran | ||
| چکیده | ||
| In this article, we have implemented Sumudu transform iteration method as a new approximate analytical technique for solving fractional diffusion-wave equations. The fractional derivative is described in the Caputo sense. The solution existence, uniqueness, stability and convergence of the proposed scheme is discussed. Finally, the validity and applicability of our approach is examined with the use of a solvable model method. The results presented here are in compact and elegant expressed in term of Mittag-Leffler function which are suitable for numerical computation. | ||
| کلیدواژه‌ها | ||
| Sumudu transform؛ Diffusion-wave equation؛ Caputo fractional derivative؛ Mittag-Leffler function | ||
| مراجع | ||
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[1] O. P. Agrawal, A general solution for a fourth-order fractional diffusion-wave equation defined in a bounded domain, Computers and Structures 79 (2001),1497–1501. [2] F. B. M. Belgacemand, A. A. Karaballi, Sumudu transform fundamental properties investigations and applications, Journal of Applied Mathematics and Stochastic Analysis, 2006,Article ID 91083, (2006), 1-23. [3] V. B. L. Chaurasia, J. Singh, Application of Sumudu transform in Schr¨odinger equation occurring in quantum mechanics, Applied Mathemati-cal Sciences 4 (2010), 2843-2850. [4] A. Golbabai, K. Sayevand, Fractional calculus - A new approach to the analysis of generalized fourth-order diffusion-wave equations, Comput. Math. Appl., 61 (2011), 2227–2231. [5] A. Golbabai, K. Sayevand, Analytical treatment of differential equations with fractional coordinate derivatives, Comput. Math. Appl., 62 (2011), 1003–1012. [6] E. Hesameddini, H. Latifizadeh, Reconstruction of variational iteration al-gorithms using the Laplace transform, Int. J. Nonlinear Sci. Numer. Simul.10 (2009), 1377-1382. [7] A. A. Kilbas, A. A. Koroleva, S.V. Rogosin, Multi-parametric Mittag-Leer functions and their extension, Fract. Calc. Appl. Anal., 16 (2) (2013),378-404. [8] V. Kiryakova, The multi-index Mittag-Leer functions as an important class of special functions of fractional calculus, Comput. Math. Appl., 59 (2010),1885-1895. [9] F. Mainardi, The fundamental solutions for the fractional diffusion-wave equa-tion, Appl. Math. Lett., 9 (1996), 23–28. [10] I. Podlubny, Fractional differential equations, Academic Press, San Diego,1999. [11] K. Sayevand, A. Golbabai, Ahmet Yildirim, Analysis of differential equa-tions of fractional order, Appl. Math. Model., 36 (2012), 4356–4364. [12] K. Sayevand, K. Pichaghchi, Successive approximation: A survey on stable manifold of fractional differential systems, Fract. Calc. Appl. Anal., 18 (3)(2015), 621–641. [13] J. Tenreiro Machado, V. Kiryakova, F. Mainardi, Recent history of fractional calculus, Commun. Nonlinear Sci. Numer. Simu., 16 (2011), 1140–1153. | ||
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