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**Modified step variational iteration method for solving fractional biochemical reaction model.**
*(English)*
Zbl 1222.65111

Summary: A new method called the modification of step variational iteration method (MoSVIM) is introduced and used to solve the fractional biochemical reaction model. The MoSVIM uses general Lagrange multipliers for construction of the correction functional for the problems, and it runs by step approach, which is to divide the interval into subintervals with time step, and the solutions are obtained at each subinterval as well adopting a nonzero auxiliary parameter \(\hbar\) to control the convergence region of series’ solutions. The MoSVIM yields an analytical solution of a rapidly convergent infinite power series with easily computable terms and produces a good approximate solution on enlarged intervals for solving the fractional biochemical reaction model. The accuracy of the results obtained is in a excellent agreement with the Adam Bashforth Moulton method.

### MSC:

65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |

92E20 | Classical flows, reactions, etc. in chemistry |

35K57 | Reaction-diffusion equations |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |

35C10 | Series solutions to PDEs |

35R11 | Fractional partial differential equations |

### Keywords:

comparison of methods; numerical examples; step variational iteration method; fractional biochemical reaction model; convergence; series’ solutions
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\textit{R. Yulita Molliq} et al., Int. J. Differ. Equ. 2011, Article ID 514384, 12 p. (2011; Zbl 1222.65111)

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