On Fractional Derivatives and Primitives of Periodic Functions
On Fractional Derivatives and Primitives of Periodic Functions
We prove that the fractional derivative or the fractional primitive of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:math>-periodic function cannot be a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mo>~</mml:mo></mml:mover></mml:mrow></mml:math>-periodic function, for any period<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mo>~</mml:mo></mml:mover></mml:mrow></mml:math>, with the exception of the zero function.