Journal
ADVANCES IN DIFFERENCE EQUATIONS
Volume 2019, Issue 1, Pages -Publisher
SPRINGEROPEN
DOI: 10.1186/s13662-019-2313-z
Keywords
Modified fractional variational iteration method; Caputo derivative; Fractional nonlinear Schrodinger equation; Exact solutions; Approximate solutions
Categories
Funding
- National Nature Science Foundation of China [61070231]
- Jiangsu university students practical innovation training program guidance project of Jiangsu Province [201811276060X, 201911276109H]
- Natural science research projects of Institutions of higher learning in Jiangsu Province [18KJB110013]
- Nanjing Institute of Technology [ZK201513, CKJB201709]
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In this paper, by introducing the fractional derivatives in the sense of Caputo, the modified general mapping deformation method (MGMDM) and the modified fractional variational iteration method (MFVIM) are applied to obtain some exact and approximate solutions of the variable-coefficient fractional Schrodinger equation (VFNLS) with time and space fractional derivatives. With the aid of symbolic computation, a broad class of exact analytical solutions and their structure of the VFNLS are investigated. Furthermore, the approximate iterative series showed that the MFVIM is powerful, reliable and effective when compared with some traditional decomposition method in searching for the approximate solutions of the complex nonlinear partial differential equations with variable coefficients and fractional derivatives.
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