The non-classical calculi such as q-calculus, fractional calculus and q-fractional calculus have been hot topics in both applied and pure sciences. Then some new linear and nonlinear models have appeared. This study mainly concentrates on the analytical aspects, and the variational iteration method is extended in a new way to solve an initial value problem.
A new Adomian decomposition method is proposed to approximately solve fractional differential equations. The iteration procedure is based on a fractional Taylor series. An example is illustrated to show the presented method's efficiency and convenience.
Analytical solutions of fractional differential equations of two point value problems are considered. An equivalent integral equation of fractional order is used. The nonlinear term is linearized by Adomian polynomials. Approximation solutions are given successively and the error analysis is given. The results show that the new way is simple and efficient.