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Chebyshev spectral collocation methods (known as El-Gendi methods-as described by El-Gendi in 1969 and Mihaila and Mihaila in 2002) are presented to deal with some nonlinear evolution equations including the Korteweg-de Vries (KdV), the modified KdV, ...

An initial value problem for nonlinear fractional differential equations is considered. Using an integral equation reformulation of the initial value problem, some regularity properties of the exact solution are derived. On the basis of these properties,...

In this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we ...