Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations. (English) Zbl 1192.65092

Summary: We are concerned with a multi-term nonlinear fractional differential equation. Two methods are used to solve this type of equations. The first is an analytical method: the Adomian decomposition method. A convergence analysis of this method is discussed. This analysis is used to estimate the maximal absolute truncated error of the Adomian series solution. The second method is the proposed numerical method. A comparison between the results of the two methods is given. One of the important applications of these equations is the Bagley-Torvik equation.


65L05 Numerical methods for initial value problems involving ordinary differential equations
34A08 Fractional ordinary differential equations
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