New Families of Solutions for the Space Time Fractional Burgers Equation

TL;DR

This paper applies the hyperbolic tangent function method and Bäcklund transformations to find new exact solutions for the space-time conformal fractional Burgers equation, analyzing its integrability properties.

Contribution

It introduces new solution techniques and generates numerous exact solutions for the fractional Burgers equation, expanding the understanding of its solution space.

Findings

The equation possesses the Painleve property.

Numerous new exact solutions were constructed.

The hyperbolic tangent method is effective for fractional PDEs.

Abstract

In this paper, the hyperbolic tangent function method is applied for constructing exact solutions for space-time conformal fractional Burgers equation. Furthermore, the space-time conformal fractional Burgers equation is tested for the Painleve property and consequently new numerous exact solutions are generated via Backlund transform.