Chaos is described as a unstable dynamic behavior with dependence on initial conditions. The control and synchronization of chaotic systems requires the knowledge of parameters in advance. Recently researcher's has been shifted from integer order chaotic system to fraction order chaotic system. In this work, based on the stability theory of integer-order linear systems and Lyapunov stability theory, we present some control schemes to achieve a new type of synchronization called inverse generalized synchronization between different dimensional integer and fractional-orders chaotic systems. The effectiveness of the proposed approaches are verified by two numerical examples.