Exploring dynamical patterns and optical solutions of space-time fractional-order double-chain deoxyribonucleic acid model with Atangana's conformable derivative.

DNA, or deoxyribonucleic acid, exists in every human cell, including hair, blood, and skin, carrying the genetic blueprint for all living organisms. Comprised of two strands with four nucleotides-adenine (A), thymine (T), cytosine (C), and guanine (G)-DNA forms a double-helix structure that encodes species-specific traits. Its ability to store data and perform logical operations makes it crucial for biological research, particularly in genome sequencing, which involves complex nonlinear mathematical models. To address these challenges, nonlinear partial differential equations (NPDEs) effectively model DNA's dynamic behavior. The Atangana's conformable derivative accommodates memory effects and nonlocal properties, which are crucial in describing the viscoelastic and hereditary nature of biological systems such as DNA. Unlike integer-order derivatives, this approach captures the complexity of the molecular interactions and relaxation phenomena observed in DNA dynamics. Recent literature has supported the use of fractional models for DNA due to their ability to reflect real-world phenomena more accurately (e.g., base pair opening and long-range interactions). In this study, we explore fractional-order derivatives using Atangana's conformable derivative, applying the