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Many electrical systems can be characterized more authentically by fractional order dynamic systems. The Caputo–Fabrizio and the Atangana–Baleanu fractional derivatives have solved the singularity problem in the Caputo derivative. This work uses Caputo–Fabrizio and Atangana–Baleanu fractional derivatives to model the fractional order Buck-Boost converter in the time domain. On this basis, the mean values of output voltage and inductor current are calculated. The characteristics of Buck-Boost with different orders in different fractional derivatives are analyzed. The results indicate that the Caputo–Fabrizio and Atangana–Baleanu fractional derivatives can be applied to the Buck-Boost converter to increase the design degree of freedom, which provides more choices for describing the nonlinear characteristics of the system. • C–F and A–B derivatives are applied to Buck-Boost converters. • The effects of fractional order on output voltage and current are analyzed. • The differences between the two definitions of converters are analyzed. [ABSTRACT FROM AUTHOR]