M. Alquran, Mohammed Ali, Kamel Al-khaled, G. Grossman
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引用次数: 0
Abstract
Abstract In this study, the Caputo-type fractional time-derivative is simulated by inserting a proportional time-delay into the field function of the perturbed-KdV equation. Two effective methods have been adapted to obtain analytical solutions for this model. Then, independently, the effect of the fractional derivative and the proportional delay on the topological shape of the pKdV propagation was extrapolated. The significant conclusions of the current article reveal that the fractional derivative plays the same role as the presence of a proportional delay in the time coordinate if it is assigned as a substitute for it. With this, from a practical mathematical point of view, we have provided one of the geometric explanations of the fractional derivative. Finally, via the obtained approximate solution, we studied the impact of the perturbed coefficient on propagating the waves of the proposed KdV model.
期刊介绍：
The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.
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