A novel iterative method for solving systems of fractional differential equations.

*(English)* Zbl 1271.34003
Summary: The Reconstruction of Variational Iteration Method (RVIM) technique has been successfully applied to obtain solutions for systems of nonlinear fractional differential equations: ${D}_{*}^{\alpha}{x}_{i}\left(t\right)={N}_{i}(t,{x}_{1},\cdots ,{x}_{n})$, ${x}_{i}^{\left(k\right)}={c}_{k}^{i}$, $0\le k\le \left[{\alpha}_{i}\right]$, $1\le i\le n$, where ${D}_{*}^{\alpha}$ denote Caputo fractional derivative. The RVIM, for differential equations of integer order is extended to derive approximate analytical solutions for systems of fractional differential equations. Advantage of the RVIM, is simplicity of the computations and convergent successive approximations without any restrictive assumptions or transform functions. Some illustrative examples are given to show the validity of this method for solving linear and nonlinear systems of fractional differential equations.

##### MSC:

34A08 | Fractional differential equations |

34A45 | Theoretical approximation of solutions of ODE |

34A34 | Nonlinear ODE and systems, general |