Abstract
To explore the application of improved variational iterative method in solving fractional differential equations and the effect of DNA coding algorithm based on logistic chaos mapping in image encryption, combining Chebyshev polynomial with variational iterative method, a new algorithm for solving fractional differential equations is proposed. In order to solve the initial value problem, the simulation software is used to compare the approximate solution after the change of values of a and k in the solution process to investigate the influence of different parameters on the accuracy of fractional order system. Subsequently, the logistic chaos sequence is used to generate discrete binary sequences, and an image encryption algorithm based on DNA coding is proposed. In order to verify the encryption performance of the proposed algorithm, Matlab simulation software is used to simulate and verify the image encryption processing. The results show that when a approaches 1, the solution is closer to the exact solution than that when a approaches 0.5, 0.7, and 0.9; compared with 1, 3, 5, and 7, the constructed algorithm has the highest accuracy when k value is 9. The simulation results of the fuzzy partial fractional order system show that the chaotic sequence is sensitive to the initial value, and the logistic mapping sequence is suitable for the information encryption of the secure communication system. The simulation results of the image encryption algorithm based on DNA coding show that the algorithm can effectively encrypt the image, and the image histogram after encryption is approximately a horizontal line; slight changes in the initial value will affect the decryption effect of the image; the correlation analysis results show that there is no correlation between adjacent pixels in the image after encryption, which indicates that combining Chebyshev polynomials with variational iteration method can reduce the computational burden and improve the computational accuracy, and the image encryption algorithm proposed in this study can improve the reliability and security of image encryption.