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2000 Mathematics Subject 2008 Juliusz Schauder Adomian decomposition method Analysis Journal analytical Appl Application approximate solution assume assumptions attractors Banach space Belendez boundary value problems Center for nonlinear Center Volume 31 Chaos Solitons Fractals coincidence compact Comput consider continuous converges corrector D. D. Ganji defined Definition denote duality mapping E-mail address equation 1.1 equations of fractional exact solution exists fractional order Fredholm operator function homeomorphism homotopy perturbation method implies initial conditions Internat Juliusz Schauder Center KdV equation Lemma Maslov index Math Mathematics Subject Classification measures method for solving Methods in Nonlinear Moreover Nonlinear Analysis Journal nonlinear equations nonlinear problems Nonlinear Sci nonlinear Studies Numer obtained orientation pair partial differential equations perturbation technique Phys Proof Proposition reaction-diffusion equations satisfies Schauder Center Volume sequence Simul strongly nonlinear subset Theorem 3.1 tion Topological Methods variational iteration method weakly