Analytical Study of Fractional Dna Dynamics in the Peyrard-Bishop Oscillator-Chain Model

Abstract

In this research, we present a new auxiliary equation approach, which uses two distinct fractional derivatives: /3- and M-truncated fractional derivatives to explore the space-time fractional Peyrard-Bishop DNA dynamic model equation. This examines the nonlinear interplay between neighboring displacements and hydrogen bonds through mathematical modeling of DNA vibration dynamics. The solutions are tasked with examining the nonlinear interaction among neighboring displacements of the DNA strand. The generated solutions exhibit various wave patterns under varying fractional values and parametric conditions: w-shape, bright, combined periodic wave solutions, dark-bright, bell shaped, m-shaped, w-shaped with two bright solutions, and m-shape with two dark solutions. Graphical representations provide a complete analysis of these physical features. The results demonstrate the successful implementation of the proposed approach, which will be advantageous for locating analytical remedies to more nonlinear challenges.