Fractional derivative of Hermite fractal splines on the fractional-order delayed neural networks synchronization

• Published in: Communications in nonlinear science & numerical simulation 2025-01, Vol.140, p.108399, Article 108399
• Main Authors: Mohanrasu, S.S., Priyanka, T.M.C., Gowrisankar, A., Kashkynbayev, Ardak, Udhayakumar, K., Rakkiyappan, R.
• Format: Article
• Language: English
• Subjects: Caputo-fractional derivative; Hermite fractal interpolation function; Intermittent control; Synchronization of neural networks
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2024.108399

The purpose of this research is twofold. First, the master–slave synchronization of fractional-order neural networks is explored with time delays using aperiodic intermittent control. Then we present a sufficient condition for master–slave synchronization of delayed fractional-order neural networks via average-width intermittent control technique. A numerical simulation is used to demonstrate the efficacy of the derived results. Second, a novel investigation of the Caputo-fractional derivative of Hermite fractal splines is accomplished. Moreover, its box counting dimension is estimated and related with the Caputo-fractional order. Additionally, we propose an image encryption algorithm utilizing the semi-tensor product (STP). The efficiency of the algorithm is evaluated through the application of statistical measures. •The concept of average control width is used to address control widths globally.•This study analyzes the promising impulsive effects on intermittent synchronization.•The study of Caputo-fractional derivative is introduced on C1-Cubic Hermit FIFs.•An advanced image encryption algorithm is proposed.