Muhammad Ishfaq Khan

The primary objective of this study was to investigate the complex dynamics of coupled dispersionless equations formulated using conformable derivatives. Exact soliton solutions are first derived using the Jacobi elliptic function expansion method. These solutions were then used to train a datadriven model based on a Bayesian regularization-backpropagation neural network. The trained network is evaluated against the exact solutions through visual comparison using surface plots, contour plots, and corresponding error graphs. Furthermore, statistical metrics are computed for varying values of the conformable derivative parameter to assess the prediction accuracy and robustness. The close agreement between the predicted and exact solutions confirms the effectiveness of the proposed data-driven approach. This study highlights the potential of integrating analytical soliton solutions with neural network models to model nonlinear systems involving conformable derivatives.

In this paper, we investigate the (2+1)-dimensional complex modified Korteweg-de Vries (CmKdV) system using the conformable derivative. The CmKdV system is a beneficial model in the field of nonlinear wave theory such as fluid flow, optical communication, and plasma physics. Explicit solutions are constructed, including periodic, solitary, and shock waves form using the Jacobi elliptic function expansion method. The solutions obtained are visually presented in various dimensions using Mathematica, providing a clear physical understanding of the effects of the conformable fractional derivative. This research enhances understanding of soliton behavior in complex nonlinear systems and demonstrates the effectiveness of combining conformable derivatives with analytical methods, while also providing new insights into the dynamics and diverse forms of propagating fluid waves.

In this paper, we analyze the family of three-dimensional Wazwaz-Benjamin-Bona-Mahony (3-D WBBM) equations using the generalized Jacobi elliptic function expansion method. Understanding complicated wave patterns is critical, therefore, the family of 3-D WBBM equations is a valuable mathematical model with application in fluid mechanics, plasma dynamics, biomechanics, and engineering sciences. The main objective of this study is to build several new multiple wave form solutions for the nonlinear three-dimensional Wazwaz-Benjamin-Bona-Mahony (3-D WBBM) equations. By first using the travelling wave transformation, the nonlinear partial differential equation is transformed into an ordinary differential equation. Then the generalized Jacobi elliptic function expansion method is used to execute a finite series expansion of degree n. Due to this analytical method, we obtained numerous new exact solutions, including periodic solutions in Jacobi elliptic function forms and their corresponding Solitary and shock wave solutions in a limit convergence sense when the modulus parameter m approaches 1 and 0. These results are particularly useful for nonlinear science and mathematical physics professionals, since they provide important insights into the structure and evolution of nonlinear waves in a variety of physical circumstances. To improve the physical description of the solutions, several typical wave profiles are offered to provide a comprehensive analysis of the wave characteristics of the solutions in 2-D, 3-D, and contour visualizations were generated using accurate parameters value with the help of Mathematica. Moreover, by generating novel and accurate propagating soliton waveform solutions, the generalized Jacobi elliptic function expansion methods highlight its importance in uncovering key aspects of the model behaviours as well as suggesting potential applications in the study of water waves.

The primary objective of this work is to investigate the complex dynamics of coupled dis-persionless equations formulated with the conformable derivative. Exact soliton solutions are first derived using the Jacobi elliptic function expansion method. These solutions are then used to train a data-driven model based on a Bayesian regularization-backpropagation neural network. The trained network is evaluated against the exact solutions through visual comparison using surface plots, contour plots, and corresponding error graphs. Furthermore, statistical metrics are computed for varying values of the conformable derivative parameter to assess prediction accuracy and robustness. The close agreement between predicted and exact solutions confirms the effectiveness of the proposed data-driven approach. This study highlights the potential of integrating analytical soliton solutions with neural network models for modeling nonlinear systems involving conformable derivatives.