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Approximate analytical solutions to fractional modified KdV equations by decomposition method. (English) Zbl 1141.35047

Summary: The fractional modified Korteweg-de Vries equation (fmKdV) is introduced by replacing the first-order time and space derivatives by fractional derivatives of order \(\alpha\) and \(\beta\) with \(0< \alpha\), \(\beta\leq 1\). The Adomian decomposition method (ADM) is applied to derive explicit and numerical solutions to the fmKdV. The ADM provides analytical solutions in the form of an infinite series with easily computable components, and in some cases leads to exact solutions.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
49M27 Decomposition methods
26A33 Fractional derivatives and integrals
35C10 Series solutions to PDEs
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