An explicit and numerical solutions of the fractional KdV equation. (English) Zbl 1119.65394

Momani, Shaher

Math. Comput. Simul. 70, No. 2, 110-118 (2005).

Summary: A fractional Korteweg-de Vries (KdV) equation with initial condition is introduced by replacing the first order time and space derivatives by fractional derivatives of order \(\alpha\) and \(\beta\) with \(0 < \alpha ,\beta \leq\) 1, respectively. The fractional derivatives are described in the Caputo sense. The application of Adomian decomposition method, developed for differential equations of integer order, is extended to derive explicit and numerical solutions of the fractional KdV equation. The solutions of our model equation are calculated in the form of convergent series with easily computable components.

MSC:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53	KdV equations (Korteweg-de Vries equations)
26A33	Fractional derivatives and integrals

Keywords:

KdV equation; Adomian decomposition method; fractional calculus; numerical examples; fractional Korteweg-de Vries equation

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