Hyperbolic function solutions of time-fractional Kadomtsev-Petviashvili equation with variable-coefficients

Cheng Chen; Cheng Chen

doi:10.3934/math.2022578

AIMS Mathematics

2022, Volume 7, Issue 6: 10378-10386. doi: 10.3934/math.2022578

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Research article

Hyperbolic function solutions of time-fractional Kadomtsev-Petviashvili equation with variable-coefficients

Cheng Chen ^,

School of Science, Xi'an University of Posts and Telecommunications, Xi'an, Shaanxi 710121, China

Received: 24 November 2021 Revised: 18 March 2022 Accepted: 21 March 2022 Published: 25 March 2022
MSC : 35N10, 35R11, 83C15

Based on the variable separation method, the Kadomtsev-Petviashvili equation is transformed into a system of equations, in which one is a fractional ordinary differential equation with respect to time variable $ t $, and the other is an integer order variable coefficients partial differential equation with respect to spatial variables $ x, y $. Assuming that the coefficients of the obtained partial differential equation satisfy certain conditions, the equation is further reduced. The extended homogeneous balance method is used to find the exact solutions of the reduced equation. According to the solutions of some special fractional ordinary differential equations, we obtain some hyperbolic function solutions of time-fractional Kadomtsev-Petviashvili equation with variable coefficients.
- Riemann-Liouville,
- variable separation method,
- time-fractional,
- exact solution,
- extended homogeneous balance method
Citation: Cheng Chen. Hyperbolic function solutions of time-fractional Kadomtsev-Petviashvili equation with variable-coefficients[J]. AIMS Mathematics, 2022, 7(6): 10378-10386. doi: 10.3934/math.2022578

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Abstract

Based on the variable separation method, the Kadomtsev-Petviashvili equation is transformed into a system of equations, in which one is a fractional ordinary differential equation with respect to time variable $ t $, and the other is an integer order variable coefficients partial differential equation with respect to spatial variables $ x, y $. Assuming that the coefficients of the obtained partial differential equation satisfy certain conditions, the equation is further reduced. The extended homogeneous balance method is used to find the exact solutions of the reduced equation. According to the solutions of some special fractional ordinary differential equations, we obtain some hyperbolic function solutions of time-fractional Kadomtsev-Petviashvili equation with variable coefficients.

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