Analytical solutions of incommensurate fractional differential equation systems with fractional order 1<α,β<2 via bivariate Mittag-Leffler functions

Abstract

In this paper, we derive the explicit analytical solution of incommensurate fractional differential equation systems with fractional order 1<α,β<2. The derivation is extended from a recently published paper by Huseynov et al. in [1], which is limited for incommensurate fractional order 0<α,β<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<α,β<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.

Keywords

• incommensurate fractional order system
• bivariate mittag-leffler function
• picard's successive approximations
• analytical solutions