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Nonlinear Singular Perturbation Problems of Fractional Orders

Volume 7, Number 2 (2008)

Nonlinear Singular Perturbation Problems of Fractional Orders

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Abstract

Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and differential equations of order $\frac12$ are investigated. It is particularly shown that, whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the \emph{standard} formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order $\beta, ~0 < \beta < 1$).