@article{Ng2022, 
author = {Yong Xian Ng and Chang Phang and Jian Rong Loh and Abdulnasir Isah},
title = {Analytical solutions of incommensurate fractional differential equation systems with fractional order    1  <  α  ,  β  <  2 via bivariate Mittag-Leffler functions},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {2},
pages = {2281-2317},
keywords = {incommensurate fractional order system, bivariate Mittag-Leffler function, Picard's successive approximations, analytical solutions},
url = {https://www.sciopen.com/article/10.3934/math.2022130},
doi = {10.3934/math.2022130},
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.}
}