The Sensitive Visualization and Generalized Fractional Solitons’ Construction for Regularized Long-Wave Governing Model
Ur Rahman R. Faridi W.A. El-Rahman M.A. Taishiyeva A. Myrzakulov R. Az-Zo’bi E.A.
February 2023MDPI
Fractal and Fractional
2023#7Issue 2
The solution of partial differential equations has generally been one of the most-vital mathematical tools for describing physical phenomena in the different scientific disciplines. The previous studies performed with the classical derivative on this model cannot express the propagating behavior at heavy infinite tails. In order to address this problem, this study addressed the fractional regularized long-wave Burgers problem by using two different fractional operators, Beta and M-truncated, which are capable of predicting the behavior where the classical derivative is unable to show dynamical characteristics. This fractional equation is first transformed into an ordinary differential equation using the fractional traveling wave transformation. A new auxiliary equation approach was employed in order to discover new soliton solutions. As a result, bright, periodic, singular, mixed periodic, rational, combined dark–bright, and dark soliton solutions were found based on the constraint relation imposed on the auxiliary equation parameters. The graphical visualization of the obtained results is displayed by taking the suitable parametric values and predicting that the fractional order parameter is responsible for controlling the behavior of propagating solitary waves and also providing the comparison between fractional operators and the classical derivative. We are confident about the vital applications of this study in many scientific fields.
beta derivative , M-truncated derivative , nonlinear partial differential equation , solitary wave solutions
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Department of Mathematics, University of Management and Technology, Lahore, 54782, Pakistan
Department of Physics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia
Department of Radiation Physics, National Center of Radiation Research and Technology (NCRRT), Atomic Energy Authority, Cairo, 11787, Egypt
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Astana, 010009, Kazakhstan
Department Mathematics and Statistics, Mutah University, Al-Karak, 61710, Jordan
Department of Mathematics
Department of Physics
Department of Radiation Physics
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics
Department Mathematics and Statistics
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