alexa Picard and Adomian decomposition methods for a quadratic integral equation of fractional order


Journal of Applied & Computational Mathematics

Author(s): A M A ElSayed, Hashem HH G

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We study two analytical methods: the classical method of successive approximations (Picard method) (Curtain and Pritchard in Functional analysis in modern applied mathematics, Academic press, London, 1977) and Adomian method which gives the solution as a series (see Adomian in Stochastic system, Academic press, New York, 1983; Adomian in Nonlinear stochastic operator equations. Academic press, San Diego, 1986; Adomian in Nonlinear stochastic systems: theory and applications to physics. Kluwer, Dordrecht, 1989; Adomian et al. in J Math Comput 23:17–23, 1992; Abbaoui and Cherruault in Comput Math Appl 28:103–109, 1994; Adomian in Solving frontier problems of physics: the decomposition method. Kluwer, Dordrecht, 1995; Cherruault in Kybernetes 18:31–38, 1989; Cherruault et al. in Int J Biomed Comput 38:89–93, 1995). The existence and uniqueness of the solution and the convergence will be discussed for each method and some examples will be studied.

This article was published in Computational and Applied Mathematics and referenced in Journal of Applied & Computational Mathematics

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