Analytical solutions of incommensurate fractional differential equation systems with fractional order $1<\alpha ,\beta <2$ via bivariate Mittag-Leffler functions

In this paper, we derive the explicit analytical solution of incommensurate fractional differential equation systems with fractional order $1<\alpha ,\beta <2$. The derivation is extended from a recently published paper by Huseynov et al. in ^[1], which is limited for incommensurate fractional order $0<\alpha ,\beta <1$. The incommensurate fractional differential equation systems were first converted to Volterra integral equations. Then, the Mittag-Leffler function and Picard's successive approximations were used to obtain the analytical solution of incommensurate fractional order systems with $1<\alpha ,\beta <2$. The solution will be simplified via some combinatorial concepts and bivariate Mittag-Leffler function. Some special cases will be discussed, while some examples will be given at the end of this paper.