In this paper, a mathematical model containing two-parameter Mittag-Leffler function in its definition is proposed to be used for the first time to fit the relation between unemployment rate and inflation rate, also known as the Phillips curve. The Phillips curve is in the literature often represented by an exponential-like shape. On the other hand, Phillips in his fundamental paper used a power function in the model definition. Considering that the ordinary as well as generalised Mittag-Leffler function behave between a purely exponential function and a power function it is natural to implement it in the definition of the model used to fit the data representing the Phillips curve. The data of two strong European economies, France and Germany, are used for the modelling purposes.
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