Symmetry Classification and Exact Solutions of a Variable Coefficient Space-Time Fractional Potential Burgers’ Equation

Abstract

In this paper, we investigate the symmetry properties of a variable coefficient nonlinear space-time fractional Burgers' equation. Fractional Lie symmetries and corresponding infinitesimal generators are obtained. With the help of the infinitesimal generators some group invariant solutions are deduced. Further, some exact solutions of fractional Burgers' equation are generated by the invariant subspace method. MSC 2010: Primary 26A33: Secondary 33E12, 34A08, 34K37, 35R11, 60G22

General Response Formula for CFD Pseudo-Fractional 2D Continuous Linear Systems Described by the Roesser Model

“…In this section, we will show that the well-known Cayley-Hamilton theorem is satisfied for transition matrices (25) of CFD pseudo-fractional 2D systems described by the Roesser model (12).…”

“…Theorem 3. The solution to the system (12) for arbitrary boundary conditions (15) and an arbitrary input vector u(t 1 , t 2 ) for t 1 > 0 and t 2 > 0 is given by (30), where the transition matrices T ij for i ≥ 0 and j ≥ 0 are defined by (24) and (25).…”

“…In [24], the radial symmetry of standing waves for a nonlinear Schrödinger equation involving the fractional Laplacian and Hardy potential has been investigated. An application of Lie groups to solve the space-time fractional Burgers' equation has been presented in [25], where the authors have shown that the Lie symmetry method may be used to reduce the partial fractional-order differential equations to the system described by ordinary differential equations. Therefore, the Lie group method is one of the most effective techniques to find exact solutions of partial differential equations.…”

Lie symmetry analysis for the solution of first-order linear and nonlinear fractional differential equations

“…Due to this fact, finding an approximate solution of fractional differential equations is clearly an important task. In recent years, many effective methods have been proposed for finding approximate solution to fractional differential equations [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The purpose of this paper is solving fractional equation by Lie Symmetry method, based on conformable fractional derivative.…”

Potential Symmetries, One-Dimensional Optimal System and Invariant Solutions of the Coupled Burgers’ Equations

“…This method has a profound impact on both pure and applied areas of mathematics, physics and mechanics, etc. [2] [3] [4]. Based on the symmetries of a PDEs, many important properties of the equation such as Lie algebras [5], conservation laws [6] [7] [8], exact solutions [9] [10] [11], boundary value problem [12] can be considered successively.…”