A semi-analytical approach and theoretical investigation to multi-dimensional DNA models

The dynamics of DNA molecules play a crucial role in understanding genetic information storage, replication, and transmission. This study investigates the nonlinear dynamics of double-chain DNA systems using fractional-order differential equations, addressing the need for accurate mathematical models to capture the complex, non-local interactions inherent in biological systems. Traditional integer-order models often fail to account for memory effects and anomalous diffusion observed in DNA behavior. By employing fractional calculus, we develop a more realistic framework to model longitudinal and transverse displacements in DNA strands. The Laplace Residual Power Series Method (L-RPSM) is utilized to derive analytical solutions for (2+1)- and (3+1)-dimensional fractional DNA models, validated through numerical and graphical comparisons with exact solutions. Numerical experiments demonstrate that the method achieves absolute errors up to ${10}^{-18}$ compared with exact solutions. Our results demonstrate the efficacy of fractional calculus in capturing the nuanced dynamics of DNA, offering insights into soliton propagation and structural analysis, which are vital for applications in biophysics and genetic engineering.