Optical soliton solutions for the fractional double-chain model of DNA via the modified Sardar sub-equation method

This work extends the analytical understanding of the M-fractional double-chain model of DNA and analyzes its behavior using the modified Sardar sub-equation method (mSSEM). The proposed method is an analytical approach to establish connections between mathematical variables and the physical quantities associated with DNA. The double-chain model of DNA plays an important role in the protection and transmission of genetic data. The model is constructed of two long, elastic, and homogeneous strands that represent two polynucleotide chains of DNA molecules, connected by an elastic membrane that represents the hydrogen bonds between the base pairs of the two chains. We utilize the truncated M-fractional derivative definition, allowing for a more detailed analysis of the double-chain model of DNA's behavior. The hyperbolic, trigonometric, and exponential function solutions are found by using the mSSEM. In addition, we also give the physical representation of some presented solutions under the appropriate parameter values with 3D, 2D plots, and classify optical solitons (bright, dark, singular, bright-dark, bright-singular, periodic function, mixed trigonometric, combo, combo bright-singular). This study offers a valuable analytical tool for researchers and scientists working in nonlinear dynamics such as molecular biology, biophysics, and bioinformatics.