A trajectory tracking problem for a wheeled mobile robot, under skidding and slipping effects, is addressed. A sliding mode control scheme with fractional order reaching dynamics is proposed to solve the problem. The design of the control scheme is based on backstepping and passivity feedback equivalence techniques. The skidding and slipping effects are treated as a part of exogenous disturbances associated to a kinematic model of the robot. A formal study, based on Lyapunov stability theory, is carried out to assure the existence of a sliding surface where trajectory tracking is obtained; the same stability tool is used to study the trajectory tracking error behavior of the closed loop system. The performance of the control scheme is evaluated by means of numerical simulations and experimental results showing a good performance when compared with the corresponding integer order control scheme.