Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations

Authors:
A. M. A. El-Sayed;I. L. El-Kalla;E. A. A. Ziada
Affiliations:
Mathematics Department, Faculty of Science, Alexandria University, Alexandria, Egypt;Mathematics & Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, Egypt;Faculty of Engineering, Delta University for Science and Technology, Gamasa, Egypt
Venue:
Applied Numerical Mathematics
Year:
2010

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Abstract

We are concerned here with a multi-term nonlinear fractional differential equation (FDE). Two methods are used to solve this type of equations. The first is an analytical method; Adomian decomposition method (ADM). Convergence analysis of this method is discussed. This analysis is used to estimate the maximum absolute truncated error of Adomian's series solution. The second method is a proposed numerical method (PNM). A comparison between the results of the two methods is given. One of the important applications of these equations is Bagley-Torvik equation.