Soliton Solution of the Peyrard–Bishop–Dauxois Model of DNA Dynamics with M-Truncated and <i>β</i>-Fractional Derivatives Using Kudryashov’s <i>R</i> Function Method

Abstract

In this paper, the Peyrard–Bishop–Dauxois model of DNA dynamics is discussed along with the fractional effects of the M-truncated derivative and β-derivative. The Kudryashov’s R method was applied to the model in order to obtain a solitary wave solution. The obtained solution is explained graphically and the fractional effects of the β and M-truncated derivatives are also shown for a better understanding of the model.

Keywords

• soliton solutions
• fractional Peyrard–Bishop–Dauxois DNA model
• M-truncated and <i>β</i>-fractional derivatives
• Kudryashov’s <i>R</i> function method