New analytical wave solutions of fractional order DMBBM and Bateman-Burgers equations

Abstract

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The purpose of this article is to explore a new method for solving one of the nonlinear partial differential equations (NPDE) which is difficult to solve. The dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and the solutions of space-time fractional Bateman-Burgers equation is solved by a travelling wave analysis method as the Riccati sub-equation. The solutions of space-time fractional DMBBM equation and the solutions of space-time fractional Bateman-Burgers equation can be expressed in the forms of exponential functions, trigonometric functions, rational functions, and hyperbolic functions. The singular wave, singular kink wave, and periodic wave are the representations of the solution graphs.

Keywords

• dispersive modified Benjamin-Bona-Mahony (DMBBM) equation
• Bateman-Burgers equation
• nonlinear partial differential equation
• travelling wave analysis method
• Riccati sub-equation