We investigate the spreading characteristics of a Dirac delta wave packet in a fractional Schrödinger equation formalism. We present a phase diagram that illustrates the localized and extended states conditions. To do so, we use a split step finite difference method to solve the resulting fractional equations. We show that the strongly fractional and simultaneously strongly nonlinear systems are in insulator phase, which expresses wave packet survival. This is a valuable result because wave packet survival, which can lead to solitonic characteristics, is an important issue in the communication technologies.