Secure optical cryptographical transmission of solitons to fractal fractional Kairat model by novel approach

This study examines the dynamics of fractal solitons in fractal fractional models, which are crucial for optical communications, oceanography, and mathematical physics. The generalised form of the fractal-fractional Kairat-II model ($\mathrm{FFKM}$) is investigated using a conformable derivative, which is a fractal-fractional derivative ($\mathrm{FFD}$). The fractal fractional method of variational form ($\mathrm{FFVWM}$) is a new mathematical technique that successfully obtains certain new fractal solitons of the governing model. Additionally, to guarantee the transmission of solitons, examine the solitons using the cryptographic technique of Encryption-Decryption ($\mathrm{ED}$). This novel method has the advantages of being easy to use, efficient, and convenient. The 3-dimensional, 2-dimensional, and contour plots demonstrate the importance of these recently discovered fractal soliton solutions for expanding our understanding of physical oceanography.