Local Fractional Variational Iteration Method and Its Algorithms

Yang Xiao-Jun, Fu-Rong Zhang

Abstract


This letter investigates local fractional variational iteration method based on the local fractional integral equation and its algorithms (also called local fractional variational iteration algorithms). We first introduce the theory of local fractional derivative and integration and their fractal geometrical explanation, generalized linear operator, generalized Banach space and generalized Banach algebra. Then local fractional Volterra integral equations and variational iteration algorithms are structured based on the local fractional calculus (LFC). Finally, the convergence of local fractional variational process is proved. It is of a great significance for scientists and engineers to handle analytical solutions of linear/ nonlinear local fractional equations via local fractional operators (local fractional differential operators and local fractional integral operator).

Keywords


Variational iteration method; Variational iteration algorithms; Convergence; Fractal geometry; Local fractional calculus

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