This research presents a numerical approach to obtain the approximate
solution of the n-dimensional cohomological equations of fractional
order in continuous-time dynamical systems. For this purpose, the $ n
$-dimensional fractional M\”{u}ntz-Legendre
polynomials (or n-DFMLPs) are introduced. The operational matrix of the
fractional Riemann-Liouville derivative is constructed by employing
n-DFMLPs. Our method transforms the cohomological equation of fractional
order into a system of algebraic equations. Therefore, the solution of
that system of algebraic equations is the solution of the associated
cohomological equation. The error bound and convergence analysis of the
applied method under the $ L^{2} $-norm is discussed. Some
examples are considered and discussed to confirm the efficiency and
accuracy of our method.