Rida, S. Z.; El-Sherbiny, H. M.; Arafa, A. A. M. On the solution of the fractional nonlinear Schrödinger equation. (English) Zbl 1217.81068 Phys. Lett., A 372, No. 5, 553-558 (2008). Summary: We present the nonlinear Schrödinger (NLS) equation of fractional order. The fractional derivatives are described in the Caputo sense. The Adomian decomposition method (ADM) in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these schemes, the solution constructed in power series with easily computable components. Cited in 73 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35Q55 NLS equations (nonlinear Schrödinger equations) 35R11 Fractional partial differential equations Keywords:the decomposition method; NLS equation; numerical solution; fractional calculus PDFBibTeX XMLCite \textit{S. Z. Rida} et al., Phys. Lett., A 372, No. 5, 553--558 (2008; Zbl 1217.81068) Full Text: DOI References: [1] Bang, O.; Christiansen, P. L.; Rasmussen, F. K., Appl. Anal., 57, 3 (1995) [2] Zakharov, V. E.; Shabat, A. B., Phys. JETP, 34, 62 (1972) [3] Hasegawa, A.; Tappert, F., Appl. Phys. Lett., 23, 142 (1973) [4] Hasegawa, A., Optical Solitons in Fibers (1989), Springer: Springer Berlin [5] Mollenaur, L. F.; Stolen, R. H.; Gordon, J. P., Phys. Rev. Lett., 45, 1095 (1980) [6] Adomain, G., Solving Frontier Problem of Physics: The Decomposition Method (1994), Kluwer Academic Press: Kluwer Academic Press Boston [7] Adomain, G., J. Math. Anal. Appl., 135, 501 (1988) [8] A.Y. Luchko, R. Grorefio, The initial value problem for some fractional differential equations with the Caputo derivatives, preprint series A08-98, Fachbreich Mathematic and Informatics, Freic Univ., Berlin, 1998; A.Y. Luchko, R. Grorefio, The initial value problem for some fractional differential equations with the Caputo derivatives, preprint series A08-98, Fachbreich Mathematic and Informatics, Freic Univ., Berlin, 1998 [9] Caputo, M., Geophys. J. Roy. Astron. Soc., 13, 529 (1967) [10] Wazwaz, A. M., Appl. Math. Comput., 111, 33 (2000) [11] Mittag-Leffler, G. M., Rend. Accad. Lincei, 13, 5, 3 (1904) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.