Numerical behavior of a fractional fifth order dissipative system of magnetoconvection

In this paper, an autonomous fractional order fifth-order dissipative system of magnetoconvection 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 5M5M. 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.