Numerical behavior of a fractional fifth order dissipative system of magnetoconvection

摘要

In this paper, an autonomous fractional order fifth-order dissipative system of magneto-convection is numerically investigated in order to find its phase portraits. A fifth-order system for magnetoconvection is proposed to describe nonlinear coupling between an external magnetic field and Rayleigh-Bernard convection. An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is used. The fractional fifth-order system is converted to a system of ordinary differential equation of order 5M. Also stability analysis is studied by using the fractional Routh-Hurwitz stability conditions in origin. Numerical results show that the presented method is easy to implement and accurate to differential equations of fractional order.