New fractional matrix with its applications in image encryption

In this paper, new fractional matrix generation by using different the periodic matrix sequences are considered. For a periodic matrix with period P, its integer forms and fractional forms can constitute different periodic matrix sequences. The series of the periodic matrix sequence can be used to compute and construct different fractional matrices, which is depended on the relationship between the period and the size of the periodic matrix sequence. The proposed fractional matrix generation method is general and can be used to any periodic matrices. Then, we extend the new fractional matrices to multi-order forms, which can be used in image encryption. Simulation results and the application example in image encryption using the obtained new fractional matrix are also presented.