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Advanced wave dynamics in the STF-mBBM equation using fractional calculus
Muhammad Abdaal Bin Iqbal1, Muhammad Zubair Raza2, Aziz Khan3
1Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, 54590, Pakistan. abdaalbiniqbal040@gmail.com.
This study explores the STF modified Benjamin-Bona-Mahony equation using fractional calculus and the modified [Formula: see text]-expansion method. Researchers gained insights into wave phenomena and chaotic dynamics, offering valuable findings for future research.
Area of Science:
- Non-linear dynamics
- Fractional calculus
- Wave phenomena
Background:
- The STF modified Benjamin-Bona-Mahony (STF-mBBM) equation models phenomena like ocean waves and plasma physics.
- Fractional calculus offers advanced tools for analyzing complex wave dynamics.
Purpose of the Study:
- To investigate the STF-mBBM equation using fractional calculus and beta derivatives.
- To derive and analyze traveling wave solutions, including periodic and kink singular solitons.
- To explore the influence of the fractional parameter on wave behavior and system dynamics.
Main Methods:
- Application of fractional calculus and beta derivatives.
- Utilizing the modified [Formula: see text]-expansion method (M [Formula: see text]-EM).
- Analysis of chaotic dynamics via Hamiltonian properties and Galilean transformations for sensitivity analysis.
Main Results:
- Derivation of periodic and kink singular soliton solutions for the STF-mBBM equation.
- Graphical representation of traveling waves, illustrating the impact of the fractional parameter.
- Comprehensive sensitivity analysis (local and global) of the model's dynamics.
Conclusions:
- The study provides a thorough understanding of the fractional STF-mBBM model's non-linear dynamics.
- Findings offer novel insights into wave phenomena and chaotic behavior.
- The research presents significant contributions for future investigations in this field.
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