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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 inωx  are replaced by the Mittag-Leffler functions E α  (i(nωx) α ) , over the interval [0,M α /ω] where 0 &lt; ω &lt; ∞ and M α  &gt; 0 is the period of the function E α  (ix α ) , i.e., E α  (ix α ) = E α  (i(x +M α ) α ) .

On the Invalidity of Fourier Series Expansions of Fractional Order