This paper presents a model reference adaptive controller for linear time invariant systems 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 certain time instants. Boundedness of the signals in the resulting controlled system is proved using recent results. A simulation study is provided for a second order system to show how the proposed control strategy can improve the behavior 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. Copyright (C) 2020 The Authors.