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Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations. (English) Zbl 1298.35241

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.

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

Citations:

Zbl 1176.33023

Software:

ADMP; Maple
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Full Text: DOI