On the Singular Perturbations for Fractional Differential Equation

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact so...

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Bibliographic Details
Published in:TheScientificWorld 2014-01, Vol.2014 (2014), p.1-9
Main Author: Rusagara, Innocent
Format: Article
Language:English
Subjects:
Applied mathematics
Derivatives
Differential equations
Mathematical research
Mathematics
Methods
Ordinary differential equations
Partial differential equations
Perturbation (Mathematics)
Studies
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Summary:The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.
ISSN:2356-6140
1537-744X
1537-744X
DOI:10.1155/2014/752371