  Via chirp functions from fractional Fourier transforms, the authors introduce
fractional Riesz potentials related to chirp functions, establish their
relations with fractional Fourier transforms, fractional Laplace operators
related to chirp functions, and fractional Riesz transforms related to chirp
functions, and obtain their boundedness on rotation invariant spaces related to
chirp functions. Finally, the authors give the numerical image simulation of
fractional Riesz potentials related to chirp functions and their applications
in image processing. The main novelty of this article is to propose a new image
encryption method for the double phase coding based on the fractional Riesz
potential related to chirp functions. The symbol of fractional Riesz potentials
related to chirp functions essentially provides greater degrees of freedom and
greatly makes the information more secure.
