A Dynamical Analysis on the Solutions of Time-Fractional Rosenau-Korteweg de Vries-Regularized Long Wave Equation via Approximate Analytical Method
Abstract
Wave propagation in fluids, optical fibers and plasma physics are explained by complex math equations that include dispersion and dissipation effects. This study looks at the solutions for a specific equation that includes dispersion and regularization effects. To understand the effects of the Rosenau-Korteweg de Vries-regularized long wave equation, we used a new method called the approximate analytical method (AAM). We also proved that our solution is unique. The method uses the Caputo derivative, which helps describe how things change over time and memory effects. The solution is a series that shows how the wave behaves and converges quickly without needing to simplify or discretize the equation. We also drew plots and graphs to visualize the wave dynamics. Our method describes the behavior and accuracy of solutions and the algorithm shows that it can handle problems with nonlinearity and memory effects. We tested our method with simulations and 3D visualizations, which show that it is effective and accurate compared to results. The results confirm that our method can be used to understand fractional systems suggesting its use in many areas of science and technology.
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References
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