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Advanced fractional soliton solutions of the Joseph-Egri equation via Tanh-Coth and Jacobi function methods
Khadija Shakeel1, Dumitru Baleanu2, Muhammad Abbas1
1Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan.
Abstract:
This study introduces new exact soliton solutions of the time-fractional Joseph-Egri equation by employing the Tanh-Coth and Jacobi Elliptic Function methods. Using Jumarie's modified Riemann-Liouville derivative, a wide variety of soliton structures-such as periodic, bell-shaped, W-shaped, kink, and anti-bell-shaped waves-are obtained and expressed through hyperbolic, trigonometric, and Jacobi functions. The analysis reveals the significant impact of fractional-order derivatives on soliton dynamics, with graphical illustrations highlighting their physical relevance. This work expands the known solution space of the fractional Joseph-Egri equation, demonstrates the effectiveness of advanced analytical techniques, and provides fresh insights into the behavior of fractional nonlinear waves, with potential applications in physics and engineering.
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