title: Fractional formalism to DNA chain and impact of the fractional order on breather dynamics.
abstract: We have investigated the impact of the fractional order derivative on the dynamics of modulated waves of a homogeneous DNA chain that is based on site-dependent finite stacking and pairing enthalpies. We have reformulated the classical Lagrangian of the system by including the coordinates depending on the Riemann-Liouville time derivative of fractional order γ. From the Lagrange equation, we derived the fractional nonlinear equation of motion. We obtained the fractional breather as solutions by means of a fractional perturbation technique. The impact of the fractional order is investigated and we showed that depending on the values of γ, there are three types of waves that propagate in DNA. We have static breathers, breathers of small amplitude and high velocity, and breathers of high amplitude and small velocity.
authors.affiliation: Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.
authors.forename: Alain
authors.initials: A
authors.lastname: Mvogo
authors.affiliation: Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.
authors.forename: Timoléon Crépin
authors.initials: TC
authors.lastname: Kofané
mesh_terms: D004247:DNA / Q000032:analysis*; D009038:Motion; D017711:Nonlinear Dynamics; D013816:Thermodynamics
chemical_list: D004247:DNA