Application of variational iteration method to nonlinear differential equations of fractional order. (English) Zbl 1401.65087

Odibat, Zaid M.; Momani, Shaher

Int. J. Nonlinear Sci. Numer. Simul. 7, No. 1, 27-34 (2006).

Summary: In this paper, the variational iteration method is implemented to give approximate solutions for nonlinear differential equations of fractional order. In this method the problems are initially approximated by imposing the initial conditions. Then a correction functional for the fractional differential equation is well constructed by a general Lagrange multiplier, which can be identified optimally via variational theory. The iteration method, which produces the solutions in terms of convergent series with easily computable components, requiring no linearization or small perturbation. Some examples are given and comparisons are made with the Adomian decomposition method. The comparison shows that the method is very effective and convenient and overcome the difficulty arising in calculating Adomian polynomials.

MSC:

65L99	Numerical methods for ordinary differential equations
34A08	Fractional ordinary differential equations
34A45	Theoretical approximation of solutions to ordinary differential equations

Keywords:

variational iteration method; Adomian decomposition method; Lagrange multiplier; fractional differential equation; Caputo fractional derivative