(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The study aims to employ the dynamics of hyperbolic and solitons wave solutions to the time-fractional Estevez-Mansfield Clarkson equation, which is utilize to stimulate the optical fibre waves in communication system and image processing. The proposed method entails transforming nonlinear fractional partial differential equations into nonlinear ordinary differential equations. Various solutions for the current model are derived in the form of exponential and trigonometric functions. The 2D and 3D under some suitable values of parameters are also plotted. The accomplished solutions show that these are reliable, applicable, efficient and intricate dynamics inherent in the communication system, image processing and might be used in further works to found novel solutions for other types of nonlinear evolution equations ascending in physical science and engineering. The novelty of our result is to offer new and critical insights into the intricate wave behaviors of the time-fractional Estevez-Mansfield-Clarkson equation by illustrating the basic mechanics of the importance of waves interaction and propagation in optical fibres in deepening our knowledge about the basic physical model.