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In this note we show how a initial value problem for a relaxation processgoverned by a differential equation of non-integer order with a constantcoefficient may be equivalent to that of a differential equation of the firstorder with a varying coefficient. This equivalence is shown for the simplefractional relaxation equation that points out the relevance of theMittag-Leffler function in fractional calculus. This simple argument may leadto the equivalence of more general processes governed by evolution equations offractional order with constant coefficients to processes governed bydifferential equations of integer order but with varying coefficients. Our mainmotivation is to solicit the researchers to extend this approach to other areasof applied science in order to have a more deep knowledge of certain phenomena,both deterministic and stochastic ones, nowadays investigated with thetechniques of the fractional calculus.

A note on the equivalence of fractional relaxation equations to differential equations with varying coefficients