Lin, Yezhi; Liu, Yinping; Li, Zhibin Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations. (English) Zbl 1298.35241 Comput. Phys. Commun. 184, No. 1, 130-141 (2013). Summary: 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. Cited in 6 Documents MSC: 35R11 Fractional partial differential equations 35-04 Software, source code, etc. for problems pertaining to partial differential equations 34A08 Fractional ordinary differential equations 34-04 Software, source code, etc. for problems pertaining to ordinary differential equations 26A33 Fractional derivatives and integrals Keywords:nonlinear fractional differential equations; Adomian decomposition method; Adomian polynomials; analytic approximate solutions; initial value problems; boundary value problems Citations:Zbl 1176.33023 Software:ADMP; Maple PDFBibTeX XMLCite \textit{Y. Lin} et al., Comput. Phys. Commun. 184, No. 1, 130--141 (2013; Zbl 1298.35241) Full Text: DOI