  The purpose of this short paper is to show the invalidity of a Fourier series
expansion of fractional order as derived by G. Jumarie in a series of papers.
In his work the exponential functions $e^{in\omega x}$ are replaced by the
Mittag-Leffler functions $E_\alpha \left (i (n\omega x)^\alpha\right) ,$ over
the interval $[0, M_\alpha/ \omega]$ where $0< \omega<\infty $ and $M_\alpha$
is the period of the function $E_\alpha \left( ix^\alpha\right),$ i.e.,
$E_\alpha \left( ix^\alpha\right)=E_\alpha \left( i(x+M_\alpha)^\alpha\right).$
