A. I., Md. Ismail and Hytham. A., Alkresheh
(2016)
An algorithm for positive solution of boundary value problems
of nonlinear fractional differential equations by Adomian
decomposition method.
Journal of Interpolation and Approximation in Scientific Computing, 2016 (1).
pp. 25-37.
ISSN 2194-3907
Abstract
In this paper, an algorithm based on a new modification, developed by Duan and Rach, for the Adomian decomposition
method (ADM) is generalized to find positive solutions for boundary value problems involving nonlinear fractional
ordinary differential equations. In the proposed algorithm the boundary conditions are used to convert the nonlinear
fractional differential equations to an equivalent integral equation and then a recursion scheme is used to obtain the
analytical solution components without the use of undetermined coefficients. Hence, there is no requirement to solve
a nonlinear equation or a system of nonlinear equations of undetermined coefficients at each stage of approximation
solution as per in the standard ADM. The fractional derivative is described in the Caputo sense. Numerical examples
are provided to demonstrate the feasibility of the proposed algorithm.
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