Numerical solution of some wave equations with non-local edge conditions of fractional order in the sense of Caputo by the SOME BLAISE ABBO method (SBA)

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Résumé

In this paper, we are interested in solving some one-dimensional wave equations of fractional order β with 1<β≤2 in the Caputo sense by the SBA method.
The SBA method is based on a combination of the Adomian decomposition method, Picard’s principle and the method of successive approximations. This method uses a process that converges rapidly to the exact solution when it exists in a functional space of the problem posed.

Mots-clés

SOME BLAISE ABBO (SBA), Fractional functional equations, Caputo derivative, Riemann-Liouville integral, Non-local edge conditions, Partial differential equations