Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations. The Adomian decomposition method (ADM) is one of the most effective methods to construct analytic approximate solutions for nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials (see [R. C. Rach, Kybernetes 37, No. 7, 910–955 (2008; Zbl 1176.33023)]), the Adomian decomposition method and the Padé approximants technique, a new algorithm is proposed to construct analytic approximate solutions for nonlinear fractional differential equations with initial or boundary conditions. Furthermore, a MAPLE software package is developed to implement this new algorithm, which is user-friendly and efficient. One only needs to input the system equation, initial or boundary conditions and several necessary parameters, then our package will automatically deliver the analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the scope and demonstrate the validity of our package, especially for non-smooth initial value problems. Our package provides a helpful and easy-to-use tool in science and engineering simulations.
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References in zbMATH (referenced in 2 articles )
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- Jefferson, G.F.; Carminati, J.: FracSym: automated symbolic computation of Lie symmetries of fractional differential equations (2014)
- Lin, Yezhi; Liu, Yinping; Li, Zhibin: Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations (2013)