TY - GEN
T1 - Approximate Solutions of the Fractional Zakharov-Kuznetsov Equation Using Laplace-Residual Power Series Method
AU - Eriqat, Tareq
AU - Oqielat, Moa’ath N.
AU - El-Ajou, Ahmad
AU - Ogilat, Osama
AU - Momani, Shaher
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
PY - 2024
Y1 - 2024
N2 - An analytical solution is proposed in this work for the non-linear time-fractional Zakharov-Kuznetsov partial differential equation (FZK-PDE) in the Caputo sense. The FZK-PDE model demonstrates the behavior of weakly nonlinear ion-acoustic waves in a plasma with a uniform magnetic field. A series solution for the FZK-PDE is obtained using the so-called Laplace-Residual power series method (L-RPSM). The L-RPSM is a simple and efficient technique for obtaining approximate and exact series solution of nonlinear and linear fractional differential equations (FDEs). Graphical and numerical solutions of several test examples show the reliability and efficiency of the L-RPSM. Moreover, the results show that the L-RPSM is powerful, competitive, simple, and reliable for a wide range of fractional PDEs.
AB - An analytical solution is proposed in this work for the non-linear time-fractional Zakharov-Kuznetsov partial differential equation (FZK-PDE) in the Caputo sense. The FZK-PDE model demonstrates the behavior of weakly nonlinear ion-acoustic waves in a plasma with a uniform magnetic field. A series solution for the FZK-PDE is obtained using the so-called Laplace-Residual power series method (L-RPSM). The L-RPSM is a simple and efficient technique for obtaining approximate and exact series solution of nonlinear and linear fractional differential equations (FDEs). Graphical and numerical solutions of several test examples show the reliability and efficiency of the L-RPSM. Moreover, the results show that the L-RPSM is powerful, competitive, simple, and reliable for a wide range of fractional PDEs.
KW - Caputo fractional derivative
KW - Fractional zakharov-kuznetsov equation
KW - Laplace-residual power series method
UR - https://www.scopus.com/pages/publications/85206888033
U2 - 10.1007/978-981-97-4876-1_32
DO - 10.1007/978-981-97-4876-1_32
M3 - Conference contribution
AN - SCOPUS:85206888033
SN - 9789819748754
T3 - Springer Proceedings in Mathematics and Statistics
SP - 467
EP - 484
BT - Mathematical Analysis and Numerical Methods - IACMC 2023
A2 - Burqan, Aliaa
A2 - Saadeh, Rania
A2 - Qazza, Ahmad
A2 - Ababneh, Osama Yusuf
A2 - Cortés, Juan C.
A2 - Diethelm, Kai
A2 - Zeidan, Dia
PB - Springer
T2 - 8th International Arab Conference on Mathematics and Computations, IACMC 2023
Y2 - 10 May 2023 through 12 May 2023
ER -