Lie Symmetry Analysis, Exact Solutions, and Conservation Laws for the Generalized Time-Fractional KdV-Like Equation

Abstract

In this paper, the problem of constructing the Lie point symmetries group of the nonlinear partial differential equation appeared in mathematical physics known as the generalized KdV-Like equation is discussed. By using the Lie symmetry method for the generalized KdV-Like equation, the point symmetry operators are constructed and are used to reduce the equation to another fractional ordinary differential equation based on Erdélyi-Kober differential operator. The symmetries of this equation are also used to construct the conservation Laws by applying the new conservation theorem introduced by Ibragimov. Furthermore, another type of solutions is given by means of power series method and the convergence of the solutions is provided; also, some graphics of solutions are plotted in 3D.

Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation

“…where N x , N t are Noether operators, X (α,2) is defned by (12), and W i is the characteristic function represented as follows:…”

“…Later, Gazizov proposed the generalization of the Lie symmetry method for fractional diferential equations (FDEs) by developing prolongation formulas for fractional derivatives. Since then, numerous studies have been conducted to investigate FDEs using the Lie symmetry method, see [11][12][13].…”

Conservation laws, Lie symmetries, self adjointness, and soliton solutions for the Selkov–Schnakenberg system

“…Rashidi and Hejazi [25] in their work used LSA to attain the solutions of a fractional integro-differential system called the Vlasov-Maxwell system. Bahi and Hilal [26] used LSA to find the CLs and exact solutions of the generalized time-fractional Korteweg-de Vries-Burgers-like equation. Liu et al used LSA on generalized time-fractional diffusion equations and also derived the CLs and exact solutions of the model [27][28][29][30][31][32].…”

Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV-Like Equation

“…In [37], an inquiry was undertaken to increase the reliability and precision of a genetic programming-based method to deduce model equations from a proven analytical solution, especially by using the solitary wave solution; the program, instead of giving (2), surprisingly gave the fractional KdV-like equation. By using the KdV-like equations, we can find other properties of the classical equation (see [25,32,[38][39][40][41][42]). The paper is arranged as follows.…”