TY - JOUR
T1 - Two Novel Computational Techniques for Solving Nonlinear Time-Fractional Lax’s Korteweg-de Vries Equation
AU - Mishra, Nidhish Kumar
AU - AlBaidani, Mashael M.
AU - Khan, Adnan
AU - Ganie, Abdul Hamid
N1 - Publisher Copyright:
© 2023 by the authors.
PY - 2023/4
Y1 - 2023/4
N2 - This article investigates the seventh-order Lax’s Korteweg–de Vries equation using the Yang transform decomposition method (YTDM) and the homotopy perturbation transform method (HPTM). The physical phenomena that emerge in physics, engineering and chemistry are mathematically expressed by this equation. For instance, the KdV equation was constructed to represent a wide range of physical processes involving the evolution and interaction of nonlinear waves. In the Caputo sense, the fractional derivative is considered. We employed the Yang transform, the Adomian decomposition method and the homotopy perturbation method to obtain the solution to the time-fractional Lax’s Korteweg–de Vries problem. We examined and compared a particular example with the actual result to verify the approaches. By utilizing these methods, we can construct recurrence relations that represent the solution to the problem that is being proposed, and we are then able to present graphical representations that enable us to visually examine all of the results in the proposed case for different fractional order values. Furthermore, the results of the current approach exhibit a good correlation with the precise solution to the problem being studied. Furthermore, the present study offers an example of error analysis. The numerical outcomes obtained by applying the provided approaches demonstrate that the techniques are easy to use and have superior computational performance.
AB - This article investigates the seventh-order Lax’s Korteweg–de Vries equation using the Yang transform decomposition method (YTDM) and the homotopy perturbation transform method (HPTM). The physical phenomena that emerge in physics, engineering and chemistry are mathematically expressed by this equation. For instance, the KdV equation was constructed to represent a wide range of physical processes involving the evolution and interaction of nonlinear waves. In the Caputo sense, the fractional derivative is considered. We employed the Yang transform, the Adomian decomposition method and the homotopy perturbation method to obtain the solution to the time-fractional Lax’s Korteweg–de Vries problem. We examined and compared a particular example with the actual result to verify the approaches. By utilizing these methods, we can construct recurrence relations that represent the solution to the problem that is being proposed, and we are then able to present graphical representations that enable us to visually examine all of the results in the proposed case for different fractional order values. Furthermore, the results of the current approach exhibit a good correlation with the precise solution to the problem being studied. Furthermore, the present study offers an example of error analysis. The numerical outcomes obtained by applying the provided approaches demonstrate that the techniques are easy to use and have superior computational performance.
KW - Adomian decomposition method
KW - Caputo operator
KW - homotopy perturbation method
KW - time-fractional Lax’s Korteweg–de Vries equation
KW - Yang transform
UR - http://www.scopus.com/inward/record.url?scp=85153591515&partnerID=8YFLogxK
U2 - 10.3390/axioms12040400
DO - 10.3390/axioms12040400
M3 - Article
AN - SCOPUS:85153591515
SN - 2075-1680
VL - 12
JO - Axioms
JF - Axioms
IS - 4
M1 - 400
ER -