This paper presents a model reference adaptive controller for first order plants with unknown parameters. The adaptive laws used to estimate the controller parameters are based on fractional differential equations, whose orders are switched among a fractional value in the interval (0, 1) and 1 at a certain time instant T. Boundedness of the signals in the resulting controlled system is proved using recent results. A simulation study is provided to show how the proposed control strategy can improve the behavior of the controlled system and decrease the control energy used, compared to the classic model reference adaptive controllers and fractional order model reference adaptive controllers with non-switched adaptive laws.