Abstract
In this work, a Lie group reduction for a (2 + 1) dimensional fractional Kadomtsev-Petviashvili (KP) system is determined by using the Lie symmetry method with Riemann Liouville derivative. After reducing the system into a two-dimensional nonlinear fractional partial differential system (NLFPDEs), the power series (PS) method is applied to obtain the exact solution. Further the obtained power series solution is analyzed for convergence. Then, using the new conservation theorem with a generalized Noether’s operator, the conservation laws of the KP system are obtained.
Highlights
The dominant use of multifarious projects which are masked by fractional differential equations (FDEs), lies in the field of nano-technology, bio-informatics, control system, chemical engineering, heat conduction, ion-acoustic wave, mechanical engineering, diffusion equations and, several other sciences
The Lie symmetry method is one of the most powerful methods used to find the exact solution of nonlinear fractional partial differential system (NLFPDEs) [15,16,17,18,19,20,21,22,23]
The power series method is applied to finding an exact solution in the form of a power series of a fractional differential equation
Summary
In the field of fractional order differential equations, prevalent advancement is currently speculated. The Lie symmetry method is one of the most powerful methods used to find the exact solution of NLFPDEs [15,16,17,18,19,20,21,22,23] This technique is used to reduce the NLFPDEs into a lower dimension. The power series method is applied to finding an exact solution in the form of a power series of a fractional differential equation. The exact solutions, in the form of power series, are obtained, and the conservation laws are investigated. To find some new exact solutions to the system (2), we apply the Lie symmetry method to reduce the system into lower dimensions.
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