Exact Solutions for Space-time Fractional Peyrard-Bishop-Dauxois Model of DNA Dynamics by Using the Unified Method

Abstract

In this study, we investigated the space-time fractional order Peyrard–Bishop–Dauxois model using the unified method to derive exact analytical traveling wave solutions. By incorporating fractional derivatives, the model effectively captures memory effects and nonlocal interactions intrinsic to DNA dynamics, providing a refined representation of processes such as DNA denaturation. Notably, our analysis led to the discovery of soliton solutions, along with novel hyperbolic, trigonometric, and rational forms. These results not only deepen our understanding of the complex nonlinear behavior inherent in biological systems but also underscore the robustness and versatility of the unified method in addressing intricate fractional differential equations. The findings of this study provide a foundation for the further refinement of mathematical models and the exploration of more sophisticated fractional dynamics in molecular biology.

Keywords

• The unified method
• the Peyrard–Bishop–Dauxois model
• β−fractional derivative.

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